Crack Tip Parameters Research Articles

An adaptive extended finite element based crack propagation analysis method

In this paper, a method of crack propagation analysis based on adaptive extension finite element is proposed. This method combines adaptive mesh reconstruction technology with extended finite element method (XFEM). Firstly, the model of engineering structure is discretized with the help of mesh generation software, and the initial mesh is divided. Secondly, Construction of XFEM model, and the tip of crack strengthening function is introduced to describe the physical field properties of the crack tip. The integral equation is solved to obtain the crack tip parameters. Then, the adaptive mesh reconstruction technology is built to refine the mesh of crack tip area through the error estimation of crack tip. Finally, the SIFs at the crack tip were calculated using the interaction integral, and the path direction of crack growth was determined using the maximum circumferential tensile stress criterion. Thus, the propagation path can be well traced.

A simple, robust novel Williams series-based FE-analytical hybrid technique for evaluation of SIFs and higher order coefficients

To evaluate crack-tip parameters, various hybrid methods (HMs) amalgamating experimental domain data with multi-parameter field-variable expressions have been extensively employed. On the other hand, simpler HMs leveraging boundary contour data and demonstrating the robustness of the HMs for input data errors have been scarcely reported. In this regard, the present work addresses these gaps by proposing and illustrating a novel HM coupling coarse-mesh FE boundary displacement data on the crack lips, but not limited to it, with Williams’s series. Additionally, the HM’s robustness for simulated Gaussian error distribution in the input data is demonstrated. Comparison of HM-computed SIF values with converged FE values shows rapid convergence after 2–3 terms in the series and a certain number of retrieving points. Histogram analyses quantifying the deviations of HM-computed SIFs in the sample set indicate error tolerance within a reasonable limit for the fracture modes. These observations demonstrate the efficacy of the HM; In addition, the HM yields higher-order coefficients — accuracy of which are corroborated by comparing reconstructed field variables in the vicinity of the crack-tip with converged FEA. On the other hand, robustness analyses demonstrate that ±1σ of the data is within about 10% of error for all the modes. Thus, the proposed simple and robust HM offers a potential practical approach for evaluation of SIFs and higher order coefficients.

Investigation of low cycle fatigue crack propagation behavior of 316H steel at 550℃ based on cyclic response and damage accumulation: experiment and modelling

In the framework of the unified elastic-plastic constitutive theory, the cyclic response and damage evolution of 316H steel in the low cycle fatigue (LCF) regime was analyzed and modeled. A unified damage-coupled elastic-plastic constitutive model was established based on the results of uniaxial strain-controlled LCF tests, which includes a novel strain-based continuum damage model in the framework of the critical plane theory, an accumulative plastic strain and fatigue damage-related kinematic hardening model, and an isotropic hardening model. The comparison between the simulated and the experimental results indicated that the proposed model is efficient to precisely characterize the cyclic response throughout the whole fatigue process. The model was also used to simulate the fatigue crack growth behavior under different maximum loads and load ratios via finite element (FE) simulation. The effects of the load conditions on the crack growth rate and crack tip parameters were analyzed systematically.

On the experimental characterisation of crack tip displacement fields on nonplanar elements: Numerical and experimental analysis

In this work, a numerical and experimental study about crack tip fields characterisation on curve-cracked elements has been performed. This study combines a novel differential geometry approach combined with 3D-DIC and FEA results to determine crack-tip parameters from the displacement field on a curved cracked element. The work aims to validate and compare some aspects that cannot be addressed using 3D-DIC. SIFs for different crack lengths are determined using DIC and FEA data and compared In addition, a comprehensive comparison between experimental and numerical fields is done using an Image Decomposition technique based on Tchebichef polynomials.

The study on the influences of residual stresses on fatigue crack propagation in titanium alloy specimens

Fatigue crack growth is a harmful physical phenomenon in engineering materials that can be intensified by the presence of tensile residual stresses. In the present study, the effect of tensile residual stresses on the fatigue crack growth in single-edge notched bending specimens of Ti- 6Al-4V is studied. Mechanical residual stresses were created by applying a 4-point bending process. The residual stresses were evaluated utilizing the hole drilling approach under the ASTM E-837 standard. Fatigue crack propagation was measured by experimental test in specimens with and without initial residual stresses. A finite element analysis was conducted using commercial finite element software to study the plastic zone at the crack tip and fracture mechanic parameters. It was observed that the residual stress field is redistributed after each step of crack propagation. The tensile residual stress in front of the crack tip decreased from near yield strength to approximately 30% of yield strength. The tensile residual stresses near the yield strength in Ti-6Al-4V increased the fatigue crack propagation rate by approximately 50%.

Effects of Early-Age rheology and printing time interval on Late-Age fracture characteristics of 3D printed concrete

• Fracture of 3D printed concrete is strongly affected by rheology and printing process. • Increasing printing time interval changes rheology and decreases fracture toughness. • Time effect is stronger on fracture characteristics of interlayers than filaments. • Dynamic oscillation sweep method reveals time-dependent storage modulus and viscosity. • Novel fracture experiment using DIC measures and visualizes process zone growth. Concrete additive manufacturing, also known as 3D printing, opens tremendous opportunities in the construction industry, architectural design, defense and space exploration. As concrete is a quasi-brittle material and prone to fracture, it is crucial to understand the effect of the layer-by-layer manufacturing process, such as the variation in printing time intervals and the introduction of printing interlayers, on the fracture behavior of 3D printed concrete. This study elucidated the effects of early-age material rheology, printing time interval and printing path on the late-age load versus crack mouth opening displacement relation, fracture process zone, fracture toughness and fracture energy of 3D printed concrete materials with notch locations at interlayers vs filaments. A dynamic oscillation stress sweep method was used to reveal the time-dependency of early-age rheological parameters. A novel fracture experiment was designed to integrate a digital image correlation system to enable closed-loop control, measurement, and visualization of crack tip parameters during the rapid fracture processes along the printing interlayers or filaments. The results revealed that the fracture characteristics of 3D printed concrete are strongly influenced by its rheology and time-dependency of rheology, which is fundamentally different from normal cast concrete. Increasing the printing time interval increases the storage modulus, yield stress and complex viscosity of 3D printed concrete materials at different shear stress levels, consequently increasing the likelihood of imperfections, and thus decreasing the maximum process zone size developed at the crack tip, fracture toughness and fracture energy of 3D printed concrete. Such effects were found to be stronger on the fracture characteristics of printing interlayers than filaments.

Life prediction of P91 piping accounting for creep fatigue conditions

ABSTRACT To address the lack of available standard codes that deal with interactions between creep and fatigue, which is generally approached with a simple superposition law, the parameter associated with CFCG is introduced, under the hypothesis of partial creep strain reversal based on the creep reversal parameter . The TDFAD methodology used to predict initial crack growth during creep and creep-fatigue regime with P91 grade steel operating at 600°C is reviewed and integrated. This state-of-the-art crack tip parameter is introduced and accounts for small-scale creep, in the creep-fatigue crack propagation assessment.

Mixed Mode Fracture Assessment for Box Girder with Crack Damage under Combined Loads

The box girder is an important structure which is widely used in the ship and marine engineering but has not extensively investigated fracture problem. The paper adopts the stress intensity factor (SIF) as the crack tip parameter to carry out the mixed mode fracture assessment of the box girder structure with crack damage. The bending load, torsion load and side load are firstly introduced to study box girder crack propagation. And the related influencing factors of crack length, crack type, combined loads, etc. are investigated emphatically. In analysis, crack growth angle is also analyzed to evaluate the crack growth. The results show that different load types have different contributions to crack propagation. And combined bending and torsion loads effect may be considered adopting a linear superposition principle under transverse cracks and larger angle cracks. When the side load is added, the area near the crack upper surface will be easy to occur unstable expansion. These conclusions will provide a guiding significance to evaluate the crack propagation of box girder.

Analysis of stress fields at the crack tip and fracture resistance parameters under conditions of gradient plasticity

This paper presents a numerical analysis based on previously obtained experimental data on crack growth for P2M and 34X steels, aluminum 7050 and titanium alloy Ti-6Al-4V compact samples (CTS) with a one-sided lateral incision, within the framework of the conventional theory of strain gradient plasticity (CMSG), based on the Taylor dislocation model. In this study, the initial points of the curved crack trajectory were considered for two classical states: plane strain and plane stress with normal separation and pure shear. The constitutional equations of material behavior for CMSGP theories were introduced into the finite element computational complex and new fields of stress-strain state parameters for the conditions of strain gradient plasticity were obtained. The results of FE calculations show a significant increase in the magnitude of the true stress fields at the crack tip, taking into account the plastic deformation gradients and the internal characteristic length of the material. The numerical results also show that the singularity in the crack tip region is different for the model of gradient plasticity of deformations and depends on the mode I/II. An important conclusion regarding the numerical results regarding the parameters of the material's fracture resistance is that the new plastic stress intensity coefficients for gradient plasticity differ for plane strain and plane stress, and also show significant sensitivity to the plastic properties of the material and to the scale parameter of the intrinsic material length, which is attractive from the point of view of practical application and further fundamental research.

Investigation on Beremin parameters based on the toughness scaling model

The toughness scaling model (TSM for short) is one of the methods to correct the constraint loss of small specimens. The principle of this method is the fracture toughness conversion at equal Weibull stress. However, related research shows that this fracture toughness scaling model can only accurately estimate the characteristic toughness J0. The scaled toughness distribution of small specimens always deviates from that of the standard specimens. In response to this widespread deviation, this paper studies the factors that significantly affect Weibull stress, such as the crack tip radius and parameter calibration methods. This research aims to determine the requirements for accurate fracture toughness conversion and minimize the deviation under the existing conditions. After studying the data of three different specimens, it is found that the TSM based on equal σw/σu and Minami's calibration method can accurately convert the toughness distribution of small specimens. However, the calibrated Weibull modulus of the two specimens must be close enough. Since it is difficult to guarantee that the calibrated parameters of the Beremin model are constant, the requirements for this accurate toughness conversion are relatively harsh. However, appropriately relaxing the Weibull modulus requirements can make the toughness scaling model more comfortable to build. Although the deviation cannot be avoided, it is still significantly reduced compared to the original toughness scaling model. On the other hand, this paper found that as long as the scale J0 of small specimens is equal to the J0 of standard specimens, an accurate reference temperature estimation can be easily obtained.

Theory and experiment on true mode [formula omitted] fracturing of rocks

This paper discusses the use of the double-edge notched Brazilian disk test (DNBD) for measuring true mode II fracture toughness of rocks. The term true emphasises that in this test, not only is the crack tip loading shear-based, but also the material failure is shear-induced. Conventional mode II tests typically experience dominantly tensile failure. We introduce a fracture growth criterion that explains where and how a shear-based fracture extension occurs. Our theoretical analysis demonstrates that large values of compressive T-stress in the DNBD specimen significantly help inducing a true mode II fracturing. Crack tip parameters are computed by finite element analyses for various notch lengths and loading angles. These values are then employed to determine the geometry and loading condition for the optimal performance of the test. We also compare the DNBD with two other available tests for measuring true mode II fracture toughness, and show that the DNBD test typically has a lower contribution of mode I loading than the two alternative approaches and, therefore, better approximates the true mode II condition while at the same time being the experimentally simplest. Three types of rocks (limestone, marble and granite) were tested using the new approach and their true mode II fracture toughness is reported for two different crack lengths. The measured true mode II fracture toughness is compared with the mode I fracture toughness obtained from the semi-circular bending test.

Numerical analysis of the effect of residual stress on transient creep in SENB specimen

Many manufacturing processes can induce residual stresses in produced components for high-temperature application. Residual stresses, combined with the primary mechanical stresses, play an important role in structural integrity assessments of high-temperature components. In this paper the elastic and elastic-plastic creep behaviour of mechanically loaded shallow cracked SENB specimen in the presence of residual stress has been analyzed. The transient crack tip parameter under creep conditions, C(t), has been numerically determined at different primary mechanical stress and residual stress levels. The analysis was performed for general material properties where different plastic and creep stress exponents were systematically varied. Based on the performed analyzes, the expressions for relaxation curves of C(t) for the considered elastic creep and elastic plastic creep cases are proposed. These expressions show good agreement with the results of the numerical analysis conducted for the arbitrarily selected input data, which gives confidence in their reliable application for estimating the C(t) values of shallow cracked SENB speciemens.

Asymptotic path-independent integrals for the evaluation of crack-tip parameters in a neo-Hookean material

In this paper, we develop new asymptotic path-independent integrals for the evaluation of the crack tip parameters in a 2D neo-Hookean material. The new integrals are of both J-integral and interaction energy integral type and rely on the separation of the asymptotic boundary value problem into independent problems for each of the deformed coordinates. Both the plane stress and plane strain cases are considered. The integrals developed are used to compute the amplitude parameters of the asymptotic crack tip fields, which allows for direct extraction of these parameters from numerical results. A long strip with an edge crack under mixed loading modes is considered for both homogeneous and biomaterial cases. It is found that the asymptotic J-integrals produce good results for the first-order parameters while the interactions integrals produce good results for both the first and second-order parameters.

The finite element over-deterministic method to calculate the coefficients of crack tip asymptotic fields in anisotropic planes

This article applies the finite element over-deterministic (FEOD) method to determine the coefficients of the crack tip asymptotic fields in an anisotropic plane. This method relies on finding the best fit of the crack tip displacement equations to the displacements taken from a large number of nodes around the crack tip. We first revisit the asymptotic solution of crack tip fields in an anisotropic plane, followed by giving the exact solution of the crack tip parameters for an infinite anisotropic plane with a central crack. Using the derived displacement field, we then formulate the FEOD method to determine the crack tip parameters from a set of finite element nodal displacements. Numerical examples of cracks in finite and infinite plates are then investigated, where the FEOD results manifest a good agreement with exact or alternative numerical solutions. A convergence study is performed to examine the robustness of the methodology and the reliability of the results. By implementing a least squares error function, we also calculate the corresponding error in approximating the displacement field. The low values of errors demonstrate the high precision of the FEOD method.

Finite element analysis of road structure containing top-down crack within asphalt concrete layer

In this paper, a four-layered road structure containing a top-down crack is investigated by performing finite element analyses in ABAQUS. In this study, in addition to the vertical load of a vehicle wheel, the horizontal load as well as its position with respect to the crack is also considered in the analyses, and the crack tip parameters including stress intensity factors (SIFs) and T-stress are then calculated. Moreover, influence of elastic modulus and thickness of the pavement layers on the crack tip parameters is studied. Results show that the horizontal and vertical loads along with their position with respect to the crack, elastic modulus and thickness of the road layers influence the crack tip parameters (KI, KII and T-stress) significantly. It was also found that for the cases that the vehicle wheel is positioned near the crack plane, only the shear deformation mode is observed at the crack tip; while, for the vehicle wheel positions far from the crack, only the opening mode is observed, and between these positions, both the opening and shear deformation modes (i.e., mixed mode I/II) are observed at the crack tip.

Low cost infrared thermography for automated crack monitoring in fatigue testing

The potential of using infrared thermography in the assessment of crack-tip parameters is described. The use of microbolometers is studied specifically to establish their suitability for use in thermoelastic stress analysis (TSA) for establishing the crack-tip parameters and for automatically monitoring crack growth using temperature measurement. To compare the behaviour of the two types of infrared cameras a camera model is devised, which is used to predict the thermoelastic response. A new automatic crack growth monitoring approach is developed based on the temperature measurement from the raw thermal data collected using the microbolometer. The thermoelastic response model and the crack monitoring procedure are demonstrated on 316 L stainless steel single edge notch tension (SENT) specimens. Cracks were established in the specimens, grown and monitored using both types of infrared detector. The procedure is validated using measurements from the photon detector and it is shown that accurate stress intensity factors (SIFs) can be obtained from growing cracks using directly the live readings from the microbolometer. The procedure provides a new means for non-contact measurements in fatigue testing, establishing crack growth rate and the SIFs with the potential for actuator control.

On the use of edge cracked short bend beam specimen for PMMA fracture toughness testing under mixed-mode I/II

In this paper an inclined edge cracked short beam specimen subjected to symmetric three-point bend loading was designed and examined for conducting mixed-mode I/II fracture toughness experiments. The aspect ratio (i.e. length to width ratio) and the loading span distance are considered much lower than the other conventional cracked bend beam samples. Crack tip parameters such as stress intensity factors and T-stress were computed numerically for this specimen by several finite element analyses and it was demonstrated that the specimen is able to produce full combinations of mode I and II including pure mode II. The practical capability of the short bend beam specimen was studied experimentally by conducting a set of mixed-mode fracture tests on PolymethylMethacrylate (PMMA) as a well-known model brittle material. The critical stress intensity factors, the direction of fracture kinking and the path of fracture trajectory were investigated both experimentally and theoretically using two stress and strain-based fracture criteria. The fracture toughness of tested PMMA was decreased by moving towards mode II case due to the effect of T-stress on the fracture mechanism of the short bend beam specimen.

Comprehensive study on the crack tip parameters of two types of disc specimens under combined confining pressure and diametric concentrated forces

Stress intensity factors and T-stress of centrally cracked circular disc (CCCD) and hollow central cracked disc (HCCD) specimens with different geometric parameters under the combined diametric concentrated forces and confining pressure were calculated using Finite Element Method. The influence of crack length, crack inclination angle, aperture ratios and confining pressure on the mixed mode SIFs, T-stress and biaxiality ratio of CCCD and HCCD specimens is investigated in this paper. Compared with the HCCD specimens, CCCD specimens can more easily transform pure mode I loading to pure mode II loading. The results obtained in this paper are helpful to understand the mechanical mechanism of rock fracture under combined confining pressure and diametric concentrated forces.

An insight into mode II fracture toughness testing using SCB specimen

AbstractThe effect of friction forces between the test specimen and its bottom supports on the mode II fracture toughness values obtained using the semicircular bend (SCB) specimen is investigated. First, a number of experiments were conducted on SCB specimen in order to determine the mode II fracture toughness of polymethyl methacrylate (PMMA) according to the conventional approaches available in the literature. Three different types of supports that have been frequently employed by researchers in recent years were used to evaluate the effect of support type on the fracture loads. It was found that the friction forces between the supports and the SCB specimen have a significant effect on the value of mode II fracture toughness measured using the SCB samples. Then, the specimen was simulated using finite element method for more detailed investigation on the near crack tip stress field evolution when friction forces increase between the supports and the SCB specimen. The finite element results confirmed that the type of support affects not only the stress intensity factors KI and KII but also the T‐stress. The experimental and numerical results showed that the use of the crack tip parameters available in literature for frictionless contact between the supports and the SCB specimen can result in significant errors when the mode II experiments are performed by using the fixed or roller‐in‐grove types of supports.

Comparison of the constraint parameters in elastic-plastic fracture mechanics

To describe the effect of crack-tip constraint on the stress field for finite cracked bodies, the following most widely used constraint parameters can be employed in elastic-plastic fracture mechanics, namely, local triaxiality parameter, constraint parameter Q, the second fracture mechanics parameter A using a three-term elastic-plastic asymptotic expansion. To establish the relationship between different constraint parameters, the crack-tip stress fields are employed. Relationship between the crack-tip constraint parameters A, A2, Q and of elastic-plastic fracture mechanics is investigated.