Critical Value Of Stress Intensity Factor Research Articles

A localized stress field approach for calculating the critical stress intensity factor for an isotropic solid at atomistic scale

Crack growth initiation in brittle materials is generally studied using the stress intensity factor (SIF) since linear elasticity is assumed to be valid in the crack-tip region. The critical SIF is the SIF just before the onset of crack growth. In atomistic simulations, the “local” critical SIF is usually found indirectly by relating it to the “global” energetically calculated critical energy release rate. Since the crack growth happens at the crack tip, a method for calculating critical SIF (at a state just before crack growth initiation) directly by near-tip stress field has been implemented. The implementation of this methodology for amorphous isotropic solids is not trivial due to the random arrangement of atoms. Further, the presence of two types of elements in amorphous solids (silica is considered here) complicates the process since the volume occupied by each atom will be different (making the use of virial stress extremely complicated). In the present work, it has first been shown that the amorphous solid is indeed linear elastic isotropic by conducting various tests for finding elastic constants and showing that only two of them are independent. Then, a near-tip stress field is calculated by averaging the analytically calculated stress. The near-tip stresses in amorphous silica, validates the presence of linear elasticity beyond a small region from the crack tip. Even with the truly amorphous nature of silica, the minimum reported R2 for the inverse square-root fit (K-dominance) is around 80% at the critical state just before the onset of crack growth. The value of critical SIF calculated directly from the near-tip stresses in the present work comes out to be very close to those predicted by other indirect methods (experiments and atomistic simulations). The proposed method in the present work has a general applicability to measure the critical SIF directly using the near-tip stress field for any amorphous isotropic solid at the atomistic scale irrespective of the number of type of constituent elements.

Assessment of the Specimen Size Effect on the Fracture Energy of Macro-Synthetic-Fiber-Reinforced Concrete.

The most frequently used construction material in buildings is concrete exhibiting a brittle behaviour. Adding fibers to concrete can improve its ductility and mechanical properties. To this end, a laboratory study was conducted to present an experimental model for the specimens' size effect of on macro-synthetic fiber-reinforced concrete using variations in fracture energy. Composite concrete beams with different thicknesses and widths were made and tested under mode I to obtain (1) fracture toughness, (2) fracture energy, and (3) critical stress intensity factor values. Results indicated that by increasing the thickness and the width, fracture toughness and fracture energy were enhanced. Moreover, increasing the thickness and width of the beam led to critical stress intensity factors enhancement respectively by 35.01-41.43% and 7.77-8.09%.

Effect of Microstructure on Mechanical Properties of 2519A Aluminum Alloy in Thickness Direction

2519A aluminum alloy thick plate is a promising structural material in the field of military industries, owing to its low density, high tensile strength and excellent ballistic performance. However, the nonuniformly distributed microstructure along the thickness direction of this alloy leads to delamination cracks, which restrict its further application in light armor fields. In order to understand the mechanism of delamination cracking along the thickness direction, the effect of the microstructure on the mechanical properties of 2519A aluminum alloy in the thickness direction was investigated. The results show that the elongation and critical stress intensity factor values (ΔKcr) of the alloy in the thickness direction are 45.8% and 44.1% lower than the values in the rolling direction, respectively. The low mechanical properties of the alloy may be due to the short distance between the second phase, the weak binding force of grain boundaries and the disharmonious deformation caused by the inhomogeneous distribution of the microstructure. This study provides a basis for improving the mechanical properties and delamination cracking of the alloy along the thickness direction.

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.

Epoxidized soybean oil modified using fatty acids as tougheners for thermosetting epoxy resins: Part 1

AbstractA series of bio‐rubber (BR) reactive tougheners for thermosetting epoxy resins was prepared by grafting renewable saturated fatty acids of different chain lengths (C6‐C14) onto epoxidized soybean oil (ESO) at varying molar ratios. The tunable nature of the BR systems derives from the architecture and functionality of naturally occurring molecules. Control of BR reactivity and molecular weight by varying the degree of grafting and the chain length of the fatty acid was demonstrated. The BR‐toughened samples were prepared by blending BRs with diglycidyl ether of bisphenol A (DGEBA), Epon 828, and stoichiometrically curing the mixture using an aromatic amine hardener, diethyl toluene diamine (Epikure W). Fracture surface morphology studies showed that tuning of phase separated particle sizes was possible depending on the BR type and weight fraction. The resulting toughening effect was evaluated by measuring the fracture toughness of control and toughened polymer samples. The use of BRs significantly improved the critical strain energy release rate and critical stress intensity factor values of thermosetting polymer samples without significantly reducing Tg and modulus. In addition to toughening and adding renewable content to petroleum‐based thermosetting epoxy systems these new tougheners have low viscosity compared to common alternatives and aid ease of processing.

Relation between fracture characteristics and moisture content along longitudinal direction in a naturally drying Scots pine

The mode I critical stress intensity factor of a Scots pine beam was studied in the tangential-radial crack propagation system. The beam was naturally dried in the lab enviroment following a year and a half-long exposure to the harsh climate of Trondheim in Norway. A comparison between critical stress intensity factor values obtained by means of experimental and theoretical approaches were made. Finite Element analysis along with the critical stress intensity factor tests were carried out to identify the values in the former datasets, while to create the latter datasets, a modified relation, on the basis of The ASTM 399–20 Standard, was propsed. The values in the above mentioned datasets, were in close correspondence together. Furthermore, the moisture content within the radial and longitudinal directions of the beam using the relative humidity and response time of the samples was studied. Finally, the relation between the moisture content and the critical stress intensity factor along the length of the beam was investigated and compared with the reported data in the literature. It was found that the pre-experimental conditioning of the wood and crack directionality system had a considerable impact on the values of critical stress intensity factor.

An improved crack-bridging model for rigid particle-polymer composites

The incorporation of rigid particles is a promising design strategy to enhance the fracture toughness of polymeric materials. Quantitatively evaluating the toughening effect of particles is crucial for thoroughly exploring the full potential of such a strategy. In this paper, an improved crack-bridging model is proposed to correlate the fracture toughness of rigid microparticle-reinforced polymer composites with their microstructure. The critical stress intensity factor (SIF) is used to describe the fracture toughness of composites. The critical SIF values of composites rely on the critical SIF of the polymer matrix and the SIF induced by the bridging particles. The discrete bridging forces induced by particles are treated as the continuous bridging stresses. The bridging-SIF is determined by the integration of bridging stress. Theoretical predictions revealed that increasing the particle volume fraction and the particle-matrix interfacial strength can effectively improve the fracture toughness of polymeric materials. For the polymer reinforced with micron-sized particles, the fracture toughness increases with increased particle size. The theoretical results predicted by our model agree well with the experimental data. Our results help to elucidate the dependence of the fracture toughness of particle-polymer composites on their microstructure and therefore are useful for the design and optimization of advanced composite materials.

Structure and properties evaluation of epoxy resin modified with polyurethane based on polymeric MDI and different polyols

The present work investigates the properties and structure of epoxy resin (EP) modified with polyurethane (PUR). This latter was prepared using polymeric diphenylmethane diisocyanate and polyethylene glycol (PEG 400) or polyoxypropylene diol with different molecular weights (POPD 1002 and POPD 2002). It was confirmed that 5% of either PUR improved significantly the mechanical properties of EP. Impact strength and critical stress intensity factor values of modified epoxy compositions were increased by 200 and 100%, respectively, relative to pristine samples. Fourier-transform infrared spectra confirmed the occurrence of chemical reactions between reactive groups of EP and PUR. The fracture surface of EP modified with PUR based on PEG exhibited less plastic yielding, while river-like lines with more pronounced plastic deformations were shown by EP modified with 5% PUR with longest chains.

Numerical Computation of Stress Intensity Factors in Ultrasonic Very-High-Cycle Fatigue Tests

The correct computation of the Stress Intensity Factor (SIF) in ultrasonic Very-High-Cycle Fatigue (VHCF) loading conditions is a key issue when investigating the crack growth rate curve with pre-cracked specimens or when evaluating critical SIF values from fracture surfaces of failed specimens. Dynamic conditions related to the resonance of the vibrating specimen, contact nonlinearity between crack faces and stress singularity at the crack tip make the SIF computation difficult and cumbersome. Generally, numerical computation through Finite Element Models (FEMs) under non-linear dynamic conditions makes use of direct integration methods (implicit or explicit). However, in the high frequency regime of ultrasonic VHCF tests, the procedure may lead to an unacceptable computational time. In order to reduce the computational time, a hybrid procedure based on the Harmonic Balance Method (HBM) and on the Virtual Crack Closure Technique (VCCT) is originally presented and applied in this paper. The dynamic field parameters calculated with the HBM are used as input data for the computation of the SIF through the VCCT.

Method of Analytical Calculation of Critical Stress Intensity Factor and its Application in CAE System

Background/Objectives: Current importance of the study is stipulated by the high costs associated with ASTM E-399 field trials. The aim is to develop the new method to avoid or reduce them. Methods: The principle methods applied to the investigation of this problem are as follows: calculation of the critical value of stress intensity factor (SIF) employing analytical method and making use of the phySIFal and mechanical properties of the materials; calculation of SIF critical value experimentally, according to standard ASTM E-399 requirements. The study is accomplished with the verification tasks that prove the workability of the method and with the results of its implementation within the prototype software (PS). The PS belongs to Computer-Aided Engineering (CAE) systems and is applied to solve the issues of fracture strength and cracking resistance. Findings: The study presents the new method founded on the application of the modified Murakami formula to calculate the critical value of SIF. There is a new algorithm that explains the functions of the PS. The algorithm consists of two parts. The first part considers the structure without cracks; the second part describes the structure with a crack. The second part of the algorithm has a block that includes the modified formula for calculating the critical value of SIF. The new method of analytical calculation of the critical SIF holds for quasi-brittle materials (plasticity zone at the top of the crack is no larger than 20 %), and it takes into account the cracks in continual three-dimensional environment. It is used for the 1st type crack. This method in combination with the relevant PS is an innovation in the sphere of strength and cracking resistance analysis, insofar as it helps either reduce or avoid the costs associated with the field tests. Applications/Improvements: The materials of the study are of practical importance for industrial companies, educational and scientific institutions that study the issues of fracture strength and cracking resistance.

Development of Mathematical Model for Detection of Conditional Sizes Primordial Cracks in LEFM and its Implementation in Russian Cax System

This paper addresses the definition of conventional primordial crack size by solving the inverse problem of traditional LEFM and implementation of this tool in the Russian CAx system APM WinMachine. The condition of the primordial origin of the crack with the principal stresses and classical criteria of strength are shown. A mathematical model for finding the conditional size of the crack is shown. The critical value of the parameter of fracture mechanics – the stress intensity factor (SIF) and the value of the stress concentrator are used for this purpose. The critical value of SIF was defined by experiment. A mathematical model has been implemented in the Russian CAX system APM WinMachine which uses a numerical finite element method (FEM). Output data (crack dimensions) of the mathematical model are used in solving the analytical problem to determine the SIF. The validity of the numerical and analytical calculation of the data is checked by comparing the SIF critical value obtained experimentally, with the analytical one. The calculations were performed on the example of solving the static problem with a different loading step.

Interaction and properties of epoxy‐amine system modified with poly(phthalazinone ether nitrile ketone)

ABSTRACTAn epoxy based on the tetraglycidyl 4,4′‐diaminodiphenyl‐ methane (TGDDM)/bisphenol A type novolac(F‐51) cured with 4,4′‐diaminidiphenysulfone (DDS) has been modified with Poly (phthalazinone ether nitrile ketone)(PPENK). The interaction between the PPENK and epoxy resin have been investigated by differential scanning calorimetry (DSC), FT‐IR, and dynamic mechanical analysis (DMA). The thermal and mechanical properties were characterized by thermogravimetric analysis (TGA), thermomechanical analysis (TMA), flexural, impact strength, and the critical stress intensity factor tests. The results showed that a large number of physical crosslinks formed by intermolecular and intramolecular hydrogen bonding indeed existed in the TGDDM/F‐51/PPENK blends. These interactions gave good compatibility between PPENK and epoxy resin. So that any phase separation had not been detected by DMA and scanning electron microscope (SEM). Beyond that the interaction could also be a benefit to the thermal and mechanical properties. Compared with the neat epoxy resin, the critical stress intensity factor values reached the maximum at 10‐phr PPENK, as well as the impact strength. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016, 133, 42938.

Effect of urethane functionality and number of epoxide groups on cure and mechanical behaviors of epoxy resins

We report the synthesis of the novel bi- and tetrafunctional epoxy resins, 2-ECI and 4-ECI, containing urethane functionality. Their chemical structures were characterized by Fourier transform infrared spectroscopy (FTIR) and 1H nuclear magnetic resonance (1H NMR) spectroscopy. The effects of urethane functionality and the number of epoxide groups on the curing behavior and physical and mechanical properties of the epoxy resins were investigated. Compared to 4-ECI, 2-ECI was more reactive with the curing agent methyl hexahydrophthalic anhydride. However, the shear strength and critical stress intensity factor values of the cured 4-ECI resin were significantly higher than those of the cured bisphenol-A diglycidylether and 2-ECI resin, which was attributed to the synergistic effects of urethane functionality and high cross-linking density in the cured 4-ECI resin.

Impact properties of glass-fiber/polypropylene composites: The influence of fiber loading, specimen geometry and test temperature

Glass fiber reinforced polypropylene composites were compounded with a twin-screw extruder and injection molded. Fiber length distribution study showed that more fiber degradation occurred during processing of the composites with higher fiber loading. Dynamic mechanical analysis carried out showed that magnitudes of storage and loss modulus of composites are improves with the presence of the glass fiber in the system. The incorporation of fibers into the composites has slightly shifted the glass transition temperature to lower values. On the other hand, the presence of the glass fiber reduces the magnitude of tan δ at α-transition dramatically due to the strengthening effect by the fibers. From impact test, it was found that increment in glass fiber loading leads to an increase in peak load, critical strain energy release rate and critical stress intensity factor indicating the improvement in the material toughness. However, there was no significant change observed in fracture energy. With respect to increasing in specimen geometry, despite an improvement in peak load and fracture energy of the impact specimen, the critical strain energy release rate and critical stress intensity factor values were decreased. On the other hand, increase in test temperature resulted in reduction of peak load and critical stress intensity factor due to increment in material ductility, whereby fracture energy and critical strain energy release rate improved.

A study of dual directional flow-formed polypropylene pipes

Flow-forming, which is also known as tube spinning or shear forming, is a cold forming, rotary-point extrusion process. Some recent publications on single-pass flow-forming of polypropylene pipes have shown that the mechanical properties are improved with increasing percentage of thickness reduction. The present research investigates the possibility to further enhance the properties of the materials by Dual directional flow-forming.The Dual directional flow-forming was achieved by two-passes forward flow-forming process on a conventional lathe, using a twin-rollers system, with a change in the spindle direction for the second pass. The effects of varying the percentage thickness reduction on the hardness, tensile and fracture toughness properties were studied at three major orientations: along the pipe axis, along the helix angle and transverse to the helix angle. The hardness of the inner and outer surfaces were found to increase with the increase in percentage thickness reduction. Along the helix direction, the yield, tensile strength and secant modulus at yield were found to increase with increasing percentage thickness reduction whilst the elongation at break decreased. In the direction perpendicular to the helix, no significant tensile property change was observed.The critical stress intensity factor values were observed to increase to twice as high for tubes flow-formed to about 70% reduction in the helix direction. In the transverse direction, the critical stress intensity factor values dropped for 50% to 60% reduction pipes to values below the unflow-formed pipes, but increased slightly to above the values of the unflow-formed pipes at 65% to 70% reduction.The microfibrillar model of oriented polymer was found to provide a satisfactory explanation to the change in mechanical properties.

Fracture mechanics of brick masonry: size effects and snap-back analysis

Fracture energy,GF, and the critical value of stress-intensity factor,KIC, are determined for brick masonry specimens tested in bending with different notch depths. The experimental results are compared with numerical simulations, obtained through a cohesive crack model developed originally for concrete. Theoretical and experimental load-deflection curves present very similar softening branches. In some cases, a snap-back instability is predicted by the model and confirmed by the experimental data. A size-scale transition appears evident from an ultimate strength collapse at the ligament to a brittle fracture due to stress-intensification. Such a transition demonstrates that LEFM is a very suitable model for brick masonry structures at the usual size-scale. A non-dimensional brittleness number is introduced as a measure of the LEFM applicability.

Comparative studies of stress-relief cracking in relaxation test specimens and in a full-scale weldment

An attempt is made to assess the susceptibility of stress-relief cracking (SRC) of simulated HAZ microstructures in heated specimens of SA508 Class 2 steel, using a notched bend relaxation test. The ability of this test to reproduce service conditions is explored by comparing cracking behaviour and the fractographic details of the cracks produced with observations made on stress-relief cracks in actual weldments of SA508 Class 2 obtained from the same manufacturer. It is shown that SRC in the relaxation test and in the weldments exhibited similar fractographic features and micromechanisms of cracking. From the test specimens, it was found that a critical value of stress-intensity factor was necessary to produce ‘severe’ cracking, and application of this value to the cracking observed in the weldments appears to be fully consistent with the details of weldment manufacture. It is proposed that a stress-intensity approach of this sort can provide a general method for the assessment of possible SRC in welded components.