Range Of Crack Lengths Research Articles

Designing the geometry of compact tension specimens for easy fracture toughness measurement using reinforcement learning

Abstract For composite laminates, a rising R-curve is observed for their fracture toughness under Mode I stress, which is important for a comprehensive failure analysis of the materials. Since it is laborious to measure the R-curve due to its dependence on both the load and the crack extension, we put forward a novel compact tension specimen by modifying its geometry to eliminate the relation between fracture toughness and crack extension, so as to simplify the experimental process of the R-curve measurement by only recording the load history. Two machine learning models were developed for the optimum sample design based on the finite element analysis of the effect of sample geometries on the R-curve. A simple neural network model was built for designing tapered specimen and a reinforcement learning model was created for further finding the best design from a broader design space. The results showed that, in contrast to the specimens with a tapered shape, which only ensure the independence between the R-curve and crack extension in the case of a small extension, the design provided by the reinforcement learning provides such independence across a wider range of crack length and an improved accuracy.

A numerical investigation of thermal stress induced cracking pattern in the solidifying nuclear fuel droplet during MFCI

During Molten Fuel Coolant Interaction (MFCI) occurring in a Sodium-cooled Fast Reactor (SFR) following a severe accident, the corium jet breaks up into coarse droplets due to hydrodynamic instabilities and fine flaked debris are generated due to the thermal stress cracking occurring on the solidifying droplet. In particular mixed oxide core debris quenched by liquid sodium are more prone to thermal stress cracking because of the excellent heat transport properties of liquid sodium, which leads to a large temperature gradient across the crust of the ceramic fuel. In this paper, thermal stress initiated cracking of solid crust of the nuclear fuel droplet is studied using Fracture Bifurcation Theory (FBT) and Minimum Potential Energy Principle (MPEP). FBT is able to predict the minimum crack length needed for crack propagation or catastrophic failure depending on the computed KI values. On the other hand, MPEP can predict the periodic and hierarchical cracking pattern that can develop on the core debris. This helps in the prediction of number of cracks and the crack length that can develop on the solid crust. Parametric studies have been carried out by varying MOX droplet sizes, crust thickness and cooling conditions and calculating KI by semi-analytical means and comparing it with KIC. The analysis revealed that solidifying droplets with radius equal to or more than 2 mm are susceptible to thermal stress initiated crack growth and catastrophic breakage even if a few tens of micron size initial crack develops on its surface. Then a particular case of 2 mm radius core debris is considered and its cracking pattern is studied by applying MPEP. This optimal crack configuration is obtained by minimizing potential energy for a given range of crack length and spacing. The analysis has been carried out with ANSYS APDL code which calculates the strain energy for a given initial crack length and spacing. The 2D computational model is validated with a similar study carried out for Alumina disc quenched in water and the results are in good agreement. The minimum fine fragment size predicted by the analysis for mixed oxide debris is a flake like debris with equivalent radius of 41 µm when approximated to be a sphere. The particle size correlates well with the fine debris sizes reported in literature of MFCI experiments.

Test method for fracture toughness GIC based on ubiquitiform theory

A new fracture toughness test method for obtaining the crack initiation fracture toughness GIC and crack propagation fracture toughness GC was proposed. This method was based on the basic idea of ubiquitiform geometry and experimental results showing that material fracture surfaces possess ubiquitiform characteristics. A uniaxial tensile test was performed on plate specimens with cracks made by ductilecast iron to generate Mode I fracture failure. Loading–displacement curves were recorded in accordance with the experimental process, and the crack-initiation work W1 and the crack propagation work W2 were recorded. The morphology of the fracture surface was observed through electron microscopy, and the ubiquitiformal complexity D of the fracture surface was calculated on the basis of ubiquitiform theory. The ubiquitiform fracture area of the fracture surface was further obtained. The formula for ubiquitiform fracture energy was provided and used to calculate the ubiquitiform fracture energies Guf1 and Guf2 of the tested material. By analyzing the relationship between the above ubiquitiform fracture energy and fracture toughness GIC, a test method for determining fracture toughness based on ubiquitiform fracture energy was proposed. The experimental fracture toughness test results for several cracks of different sizes were consistent within a certain range of crack lengths.

Calibration and validation of extended back-face strain compliance for a wide range of crack lengths in SENB-4P specimens

Compliance equations based on back-face strain or crack mouth opening displacement, and potential drop techniques are widely used to calculate fatigue crack growth rate. Standard ASTM E647 for fatigue crack growth rate testing does not include compliance based equations for single edge notched four-point bending (SENB-4P) specimens. Equations developed based on finite element (FE) analysis have been reported in literature; however, they are limited to the long crack propagation regime (i.e., relative crack length ratios a/W > 0.15). No compliance relations for crack growth in the physically short crack regime were found in literature. This work reports on a complementary numerical-experimental study towards the development of compliance equations with an extended application range in terms of relative crack length. FE simulations have been used to calibrate a back-face strain compliance equation for calculation of relative crack length in the range 0.05 ≤ a/W ≤ 0.5 for SENB-4P specimens. Four point bending fatigue tests were performed on SENB specimens extracted from 50 mm thick welded steel plates. Direct current potential drop (DCPD) for crack monitoring was used as benchmark and validation of the crack lengths determined from a back-face strain gage.

Mode II stress intensity factors for circumferential through-wall-cracked pipes under torsional loading

In this study, a systematic three-dimensional finite element analyses (3D FEA) are performed to evaluate the Mode II stress intensity factor (SIF) for circumferential through-wall cracked pipe under torsion moment. A wide range of crack lengths and pipe radius over thickness ratios are considered. Empirical solution of the mid-thickness Mode II SIF is developed as functions of crack lengths and pipe sizes. The deviating angle and the effective SIF regarding a through-wall crack (TWC) under combined bending and torsion moments are further discussed. The research outcome can provide more computational efficiency in structural integrity assessment of pressurized pipes and tubular structures.

Stress intensity factor for w-shape tension specimens

The evolution of the irradiation embrittlement of nuclear pressure vessel steels is determined experimentally using special specimen geometries. Such sub-sized w-shape eccentrically-loaded single edge cracked tension specimens are employed due to mounting and handling requirements. Stress intensity factor solutions are available in the literature for this geometry; however, they are inaccurate for smaller crack lengths. Therefore, new approximate solutions are presented in this work to determine the stress intensity factor for such a w-shape tension specimen for a wide range of crack lengths (0.05 < a/W < 0.9). Furthermore, the T-stress constraint is investigated for this special specimen design and compared with comparable designs provided in standards.

On Modeling of Vibration and Crack Growth in a Rotor for Prognostics

Prognostics and health management (PHM) include comprehensive engineering approaches that evaluate the real-time health condition of an asset and predict its future states under the actual operating conditions. This predictive ability would result in efficient maintenance approaches such as Condition Based Maintenance (CBM) that can set maintenance strategies optimally and reduce the life cycle costs. Diagnostics and Prognostics are two major concepts in PHM. Detection, Isolation and Identification of faults are done by diagnostics while prognostics deals with estimation of future states. Mechanical fatigue phenomenon that causes crack initiation and propagation is considered as a common reason for failure in mechanical parts. Hence, diagnostics and prognostics of the crack initiation and propagation have been the subject of many research papers recently.&#x0D; The current paper presents a diagnostics and prognostics method capable of detecting the crack initiation and propagation in a rotor under cyclic loading. At the first step, the coupled equations of rotor motion and crack growth are obtained. An extended model of Paris–Erdogan equation is used for crack growth modeling. The coupled equations are solved numerically. A set of features are extracted from the dynamic response of the rotor for a range of crack lengths. A dataset is compiled including features of response, operating frequency, crack length and number of cycles remained until reaching the critical crack length. With the objective of generalization of the results, the dataset is used for creating a model using an Artifical Neural Network (ANN). In the trained ANN the inputs are the operating speed and the outputs are the crack length and the remaining useful life (RUL) that address the diagnostics and prognostics objectives, respectively.

Design analysis of end notch flexure sandwich specimen with honeycomb core

Laminate beam theory based design analysis of the sandwich End Notch Flexure (ENF) test specimen is presented. The analysis is specifically considering specimens with honeycomb core, prone to in-plane compression failure of the core, other undesirable failure modes such as face indentation and core shear failure are analyzed. In addition, crack stability and energy dissipation due to frictional sliding between the crack surfaces are analyzed. Parametric analysis of ENF specimens with a range of face and core thickness, is presented to guide the design. In-plane compression failure of the core, but shorten the range of crack lengths were stable growth occurs. A thicker face will also increase the critical load for crack propagation and by so elevate the risk for indentation and core shear failures. Increased core density is beneficial for preventing indentation and core shear failures, but may increase the risk for in-plane compression failure of the core. The thickness of the core does not strongly influence the critical load for crack propagation. A thicker core increases frictional energy loss, but reduces the risk for core shear failure. A thicker core, however, makes the ENF specimen more prone to in-plane compression failure. ENF sandwich specimens with foam and honeycomb core were tested. The test results support the design analysis.

Characterization and modeling of slow crack growth behaviors of defective high-density polyethylene pipes using stiff-constant K specimen

In this study, slow crack growth (SCG) resistances of defective and normal high density polyethylene (HDPE) pipes were measured using the stiff-constant K (SCK) specimen, where the stress intensity factor (SIF) was maintained at a constant value within a certain crack length range. A significantly reduced SCG resistance was observed in the defective pipe; a detailed procedure for evaluating SCG kinetics using the SCK specimen has been provided herein. The results of a fracture surface analysis indicate that the white window patterns, resulting from poor carbon black dispersion, are the main reason for poor SCG performance. In addition, a crack layer (CL) model was derived for the SCK specimen geometry and was compared with experimental results. It was observed that the crack and process zone growth resistance parameters were significantly lower in the case of the defected pipe than those in the case of the normal pipe.

Wide‐range and accurate mixed‐mode weight functions and stress intensity factors for cracked discs

AbstractThe Wu‐Carlsson displacement‐based weight function method is extended to obtain the mode I and mode II weight functions for the edge‐ and centre‐cracked discs. Compared with Fett's direct adjustment weight functions for the edge‐cracked discs, the present weight functions are more accurate and are applicable for a wider range of crack lengths. Using the present weight functions, extensive and highly accurate mixed‐mode stress intensity factors are obtained for the cracked discs subjected to diametrically compressive forces. Assuming perfect contact and using Coulomb friction law and the present weight functions, the mode II stress intensity factors for the cracked discs with consideration of friction are obtained and widely compared with the corresponding results from finite element analyses.

Elastic-plasticJ-Tzdominance in bending and tension loadings

PurposeCrack tip stresses are used to relate the ability of structures to perform under the influence of cracks and defects. One of the methods to determine three-dimensional crack tip stresses is through theJ-Tzmethod. TheJ-Tzmethod has been used extensively to characterize the stresses of cracked geometries that demonstrate positiveT-stress but limited in characterizing negativeT-stresses. The purpose of this paper is to apply theJ-Tzmethod to characterize a three-dimensional crack tip stress field in a changing crack length from positive to negativeT-stress geometries.Design/methodology/approachElastic-plastic crack border fields of deep and shallow cracks in tension and bending loads were investigated through a series of three-dimensional finite element (FE) and analyticalJ-Tzsolutions for a range of crack lengths ranging from 0.1⩽a/W⩽0.5 for two thickness extremes ofB/(W−a)=1 and 0.05.FindingsBoth the FE and theJ-Tzapproaches showed that the combined in-plane and the out-of-plane constraint loss were differently affected by theT-stress and the out-of-plane size effects when the crack length changed from deep to shallow cracks. The conditions of theJ-Tzdominance on the three-dimensional crack front tip were shown to be limited to positiveT-stress geometries, and theJ-Tz-Q2Dapproach can extend the crack border dominance of the three-dimensional deep and shallow bend models along the crack front tip until perturbed by an elastic-plastic corner field.Practical implicationsThe paper reports the limitation of theJ-Tzapproach, which is used to calculate the state of three-dimensional crack tip stresses in power law hardening materials. The results from this paper suggest that the characterization of the three-dimensional crack tip stress in power law hardening materials is still an open issue and requires other suitable solutions to solve the problem.Originality/valueThis paper demonstrates a thorough analysis of a three-dimensional elastic-plastic crack tip fields for geometries that are initially either fully constrained (positiveT-stress) or unconstrained (negativeT-stress) crack tip fields but, subsequently, theT-stress sign changes due to crack length reduction and specimen thickness increase. TheJ-Tzstress-based method has been tested and its dominance over the crack tip field is shown to be affected by the combined in-plane and the out-of-plane constraints and the corner field effects.

An Investigation of the Enhanced Fatigue Performance of Low-porosity Auxetic Metamaterials

An experimental and numerical investigation of fatigue life and crack propagation in two-dimensional perforated aluminum structures is presented. Specifically, the performance of positive Poisson’s ratio (PPR) geometries using circular holes is compared to that of auxetic stop-hole and straight-groove hole geometries. Mechanical fatigue testing shows that the considered auxetic structures have more than 20% longer life than the porous PPR structure at the same porosity and peak effective maximum stress despite having holes with larger stress concentrations. Digital image correlation is used to detect crack initiation and damage propagation much earlier than can be detected by the unaided eye. Accompanying finite element analyses reveal that auxetic structures have the advantage over their PPR counterparts by delaying crack initiation, spreading damage over a larger area, and having a stress intensity factor that decreases over a significant range of crack lengths. In addition, numerical simulations suggest that auxetic structures maintain their negative Poisson’s ratios in the presence of cracks.

Fatigue Crack Growth Rate Behaviour of HSLA Steel at Varying Load Amplitudes

Steels for ship building applications has to possess adequate resistance to propagation of fatigue cracks, as majority of the failures in service are due to metal fatigue. In this work, the fatigue crack growth rate (FCGR) behaviour within the Paris regime of two high strength low alloy (HSLA) steels were studied. In particular the experiments were directed to reveal the effect of load ratio(R) (Tension-Tension) on the Paris law constants for the two grades of HSLA steels. Results indicated that there is an increase in Paris slope ‘m’ and decrease in Y intercept ‘C’ with increase in load ratio for both the steels. Fractography study was carried out using SEM at locations corresponding to various values of stress intensity factor in order to reveal possible reasons for acceleration of crack growth with change in R ratio from 0.1 to 0.5. It was found that secondary cracks are predominant in Steel A at a load ratio of R=0.1 as compared to R=0.5. However for Steel B, secondary cracks were found at both the load ratios. From the plot of crack growth ‘a’ vs no. of cycles ‘N’, it became evident, the number of cycles for the same range of crack length is lesser for R=0.1 than that for R=0.5 for both Steel A and Steel B. Limiting values of ‘∆K’ and ‘K’ max has been obtained for various crack growth rates ‘da/dN’ at different load ratio for steel A and steel B.

Stress intensity factors for circumferential through‐wall cracks in thin‐walled cylindrical shells subjected to tension and torsion

AbstractIn order to assess the structural integrity of tubular members or pipes containing circumferential through‐wall cracks, their stress intensity factor solutions are required. While stress intensity factors for tension and bending are available, few solutions exist for the case of torsion, even though these components may also be subjected to torque. In this paper, the finite element method is used to compute the stress intensity factors for this geometry under tension and torsion. Shell elements are employed to compute the results for thin shells by the means of the displacement extrapolation technique. The computed results indicate that the available analytical solution for torsional loading, which is based on shallow shell theory, is nonconservative for long cracks in thin shells. Shallow shell theory is in general not applicable to long cracks, and the present work is therefore able to provide solutions for a wider range of crack lengths than what is currently available.

An Algorithm for Identifying a Crack Within a Measured Displacement Field

This paper discusses an algorithm for the detection of crack damage in plate structures based on the governing differential equation (GDE) of in-plane displacement of a plate. A state-of-the-art 3D scanning laser Doppler vibrometer, which is able to provide very accurate measurements of a three-dimensional displacement field, was utilized to implement the algorithm. To evaluate the GDE from the measured displacements, a 2D Savitzky–Golay differentiating filter was used. The potential of this algorithm for detecting a crack was compared against another two algorithms which are based on displacement measurements. The first is an algorithm based on the error in smoothed to measured displacements and the other uses surface strains normalized by their mean. To investigate the efficiency of the algorithms in detecting crack damage, a number of PMMA plate specimens were fabricated with a range of crack lengths extending from a V-notch and tested under a cyclic, quasi-static, uni-axial load. For each algorithm, the crack location could be positively identified. However, the two algorithms based on the error in smoothed to measured displacements and surface strains normalized by their mean were found to be dependent on the direction of the applied load, whereas, theoretically the algorithm based on the GDE of in-plane displacement would work regardless of the direction of the applied load.

Fuzzy pattern recognition technique for crack propagation on earplate connection of guyed mast under wind load

A 2-stage damage identification technique is presented for identifying crack lengths on cable-tower connections of guyed masts. It is based on fuzzy pattern recognition theory and uses the cable force and the strain at the key locations of the earplate connection as input parameters. The methodology is developed with a numerical model under stochastic wind excitation and verified by numerical simulation and experiment. First, the relationships of cable force, strain on the connection, and crack length are explored. The wind-induced responses of guyed mast are analyzed under different wind speed and directions to form a database of cable forces. The responses of a typical connection with different crack lengths are simulated to investigate the strain sensitivity to crack propagation. Its results are used to form a second-stage strain database. The first stage of the fuzzy identification consists in identifying the interval of cable forces on the basis of cable force measurements. Then, a subjection degree function is formed between the measured strain and the developed strain database to judge the damage state of the connection by identifying the existence of a crack and estimating its length. The results of a numerical case study and further experiment are presented and show the potential and practicability of the technique to estimate the right range of crack length on earplates. Therefore, the proposed technique is practical and feasible to predict the damage state of earplate and can provide valuable prewarning information for structural safety.

Optical and analytical investigation of overloads in biaxial fatigue cracks

Structural components are often subjected to complex multiaxial loading conditions. The study of fatigue cracks under such conditions is not easy from an experimental point of view and most works tend to focus more on the simpler but less realistic case of uni-axial loading. Consequently, there are many uncertainties related to the load sequence effect that is now well known and is not normally incorporated into the growth models. The current work presents a new methodology for evaluating overload effect in biaxial fatigue cracks. The methodology includes evaluation of mixed-mode (ΔKI and ΔKII) stress intensity factor and the Crack Opening Displacement for samples with and without overload cycle under biaxial loading. The methodology is tested under two different load levels and a range of crack lengths. All crack-tip information is obtained with a hybrid optical-analytical methodology. It combines experimental full-field digital image correlation data and Williams' elastic model describing the crack-tip field.

Experimental and analytical study of cracks under biaxial fatigue

Most mechanical components experience multi-axial cyclic loading conditions during service. Experimental analysis of fatigue cracks under such conditions is not easy and most works tend to focus more on the simpler but less realistic case of uni-axial loading. Consequently, there are many uncertainties related to the load sequence effect that are now well known and are not normally incorporated into the growth models. The current work presents a new methodology for evaluating overload effect in biaxial fatigue cracks. The methodology includes evaluation of mixed-mode (KI and KII) stress intensity factor and the Crack Opening Displacement for samples with and without overload cycle under biaxial loading. The methodology is tested under a range of crack lengths. All crack-tip information is obtained with a hybrid methodology that combines experimental full-field digital image correlation data and Williams' elastic model describing the crack-tip field.

Crack-resistance diagrams of polymer composite materials in tension and compression

It is proposed to use the fracture model and the criterion equation of a generalized crackresistance diagram in two-parameter fracture macromechanics to estimate cracking resistance and construct crack-resistance diagrams of polymer composite materials in tension and compression; these fracture model and criterion equation take into account the degree of restraint of deformations near the crack tip in the form of nonsingular T-stresses. A good agreement between the experimental values of normalized stress-intensity factors and a diagram of the calculated crack-resistance of polymer composite materials has been obtained in a wide range of crack lengths using various geometry and arrangements of specimen loading for seven carbon plastics with various orderings produced by different manufacturers using pressure-chamber and infusion methods.

Mode II fracture mechanics properties of solid wood measured by the three-point eccentric end-notched flexure test

A three-point eccentric end-notched flexure test was conducted using specimens of western hemlock to determine the fracture mechanics properties under Mode II conditions while extending the crack length range for stabilising the crack propagation. The location of the loading point was varied during the test, and the effect of the loading point location on the initiation and propagation fracture toughness values was examined. With the proposed method, fracture mechanics properties were appropriately obtained at greater crack propagation lengths than in the conventional three-point end-notched flexure test when the loading point was not extremely close to the supporting point at the crack-free region.