Stress Intensity Factor KI Research Articles

Transient response of an infinite row of parallel cracks in a saturated porous medium

A method is developed for solving the transient problem of the sudden appearance of an infinite row of parallel cracks in a stretched medium of saturated porous material. The general equations of Biot’s theory in conjunction with the integral and Laplace transforms are used to reduce the problem to that of solving the Fredholm integral equation. The numerical results in terms of Mode I dynamic stress intensity factor k1 are computed for various ratios of the crack width to crack spacing to determine the interaction effect of neighboring cracks. The influence of pore fluid on the dynamic stress intensity factor is investigated by varying the values of viscosity-to-permeability ratio, and the obtained results are compared with those of the corresponding dry medium.

Numerical solutions of hypersingular integral equations for interface circular crack under axisymmetric loadings

Based on the coupled oscillatory characteristic of mode-1 and mode-2 near the interface crack tip, one kind of element for the relative displacements of the upper and lower surfaces of the axisymmetric interface crack is constructed. A universal numerical method for solving hypersingular integral equations of axisymmetric interface circular crack is established. For arbitrary normal and shear axisymmetric loadings, they are expanded into Taylor series, and the first five loadings are numerically calculated in a wide range of bimaterial constant ε=0-0.15. The detailed numerical results of the stress intensity factors K1 and K2 are given in tabular form. Comparisons with the existing exact solutions show that the numerical results in this paper have high accuracy. For arbitrary axisymmetric loadings, the stress intensity factors can be determined from the tabular numerical results by using the superposition principle.

Investigation of Mixed-Mode I/II Fracture under Impact Loading Using Split-Hopkinson Pressure Bar

Mixed-mode fracture of construction building materials under impact loading is quite common in civil engineering. The investigation of mixed-mode crack propagation behavior is an essential work for fundamental research and engineering application. A variable angle single cleavage semi-circle (VASCSC) specimen was proposed with which the dynamic fracture test was conducted by using a Split-Hopkinson pressure bar (SHPB). Notably, the mixed-mode crack propagation velocity could be detected by the synchronized crack velocity measuring system. With experimental results, the dynamic initiation stress intensity factors KI and KII were calculated by the experimental-numerical method. Additionally, the crack path of mixed-mode I/II fracture can be predicated precisely by using numerical method. Thus, a comprehensive approach of investigation on mixed-mode I/II fracture under impact loading was illustrated in this paper. The study demonstrates that the mixed-mode I/II crack would transform from complicated mode I/II to pure mode I during crack propagation, and several velocity decelerations induced crack deflection. The dynamic initiation fracture toughness of mixed-mode crack was determined by the experimental-numerical method. The VASCSC specimen has a great potential in investigating mixed-mode fracture problems with the SHPB device.

Mode I fracture toughness determination in Cu/W nano-multilayers on polymer substrate by SEM - Digital Image Correlation

Nanostructured metallic multilayers with carefully designed mechanical and functional properties are omnipresent in cutting edge technological applications. To ensure the mechanical integrity of such coatings, the Mode I critical Stress Intensity Factor KIC is used to quantify their fracture toughness in order to avoid material failure by appropriate design. In this article, we present a novel approach for the KIC determination of thin and ultrathin films on compliant substrate, based on micro-displacement field analysis using Digital Image Correlation within SEM. Using this method, KIC of a Cu/W nano-multilayer with a total coating thickness of 240 nm was determined as KIC=4.8±0.05MPam, showing excellent agreement with the values published for comparable systems in the literature. To verify the validity of the chosen approach, two independent finite element simulations were employed, thus revealing the role and effect of the compliant substrate on the stress and displacement fields arising around the crack tip in thin films.

An examination of techniques based on two strain gages for the determination of stress intensity factor [formula omitted

In this paper, Dally and Sanford [1] (DS) two strain gages technique (DS2) and a modified DS two strain gages technique (M_DS2) for accurate measurement of stress intensity factor (SIF) KI are studied. Accordingly, general finite element approaches are developed to estimate the extent of the radial locations of the strain gages in order to estimate the extent of the three- and four-term of the strain series proposed by DS. Also, to estimate the extent of validity of the proposed modified technique (M_DS2), which is a modification of the four-term strain series proposed by DS. A comparison between the results obtained by the technique of a single strain gage and the technique of two strain gages proposed by DS and the new technique is performed for four examples of configuration. Results of numerical examples show that the DS2 and M_DS2 can yield a highly accurate value of KI when the two strain gages are placed within the valid locations. Also, the results of numerical examples show that the above two strain gages techniques provide good solutions to ensure accurate measurement of KI, when the technique of a single strain gage unable to provide the desired precision and accuracy of KI in some configurations.

A phase field model for elastic-gradient-plastic solids undergoing hydrogen embrittlement

We present a gradient-based theoretical framework for predicting hydrogen assisted fracture in elastic-plastic solids. The novelty of the model lies in the combination of: (i) stress-assisted diffusion of solute species, (ii) strain gradient plasticity, and (iii) a hydrogen-sensitive phase field fracture formulation, inspired by first principles calculations. The theoretical model is numerically implemented using a mixed finite element formulation and several boundary value problems are addressed to gain physical insight and showcase model predictions. The results reveal the critical role of plastic strain gradients in rationalising decohesion-based arguments and capturing the transition to brittle fracture observed in hydrogen-rich environments. Large crack tip stresses are predicted, which in turn raise the hydrogen concentration and reduce the fracture energy. The computation of the steady state fracture toughness as a function of the cohesive strength shows that cleavage fracture can be predicted in otherwise ductile metals using sensible values for the material parameters and the hydrogen concentration. In addition, we compute crack growth resistance curves in a wide variety of scenarios and demonstrate that the model can appropriately capture the sensitivity to: the plastic length scales, the fracture length scale, the loading rate and the hydrogen concentration. Model predictions are also compared with fracture experiments on a modern ultra-high strength steel, AerMet100. A promising agreement is observed with experimental measurements of threshold stress intensity factor Kth over a wide range of applied potentials.

Research on fatigue crack propagation process of fracturing pumphead

Fracturing pumpheads are a key and crucial component in fracturing technology. Fatigue crack failure greatly decreases the pumphead working life and operational efficiency. This paper describes an analytical model for a five-cylinder fracturing pumphead using the submodel method with the re-meshing technique to analyze its fatigue crack propagation process. Changes in the crack face, a-KI curve (crack length a and stress intensity factor KI), and a-N curve (number of fatigue loading cycles N) during crack propagation are considered. The results show that the crack failure of the fracturing pumphead results primarily from mode-I cracks. During crack propagation, the curvature of the crack front gradually decreases due to the higher stress intensity factor KI at the pressured inner surfaces of the pumphead. The stress distribution on the pumphead greatly influences the change law for the a-KI curve. When the crack tip localizes in the high stress zone, KI increases with the crack length a; when the crack tip localizes in the low stress zone, KI decreases with the crack length a. The step structure of the pumphead also influences changes to the a-KI curve. Around the step structure, a wave peak appears in the a-KI curve, but the influence is localised and its effect on the a-N curve is not significant.

Mechanical Behavior of Mode I Fractured Concrete Repaired by Polymethyl Methacrylate (PMMA)

This paper attempts to investigate the fracture toughness of the cracked concrete repaired by polymethyl methacrylate (PMMA) - a thermo-plastic polymer resin. A single-edged notch beam in three-point bending test was conducted to examine the performance of cracked concrete beam after reparation. Three concrete crack widths of 1 mm, 5 mm, 10 mm were designated to be repaired and examed. The fracture properties include critical stress intensity factor KIC by Jenq and Shah and fracture energy GF by Hillerburg, were evaluated for the concrete before cracking and after reparation. Four sand contents of 0%, 10%, 20% and 40% by volume were used in the PMMA mortars. From the testing results, it appears that the load capacity and fracture toughness of repaired concrete increased with the increasing sand content. And, the PMMA mortar made repaired concrete better strength and fracture toughness as well.

Static Crack Resistance of Heat-Resistant KhN43MBTYu Nickel-Chromium Alloy in Gaseous Hydrogen

The effect of hydrogen at a pressure of up to 35 MPa and a content of up to 29 ppm on the strength, ductility, short-term and long-term static crack resistance of four KhN43MBTYu (EP-915VD) alloy modifications with different heat treatment modes and chemical composition has been studied. It has been found that the critical stress intensity factor KIc in the presence of hydrogen, just as the ductility characteristics of smooth specimens, depends on the deformation rate, reaching minimum values at rates of less than 0.1 mm/min. The fracture toughness decreases under the action of hydrogen by a factor of 2.5, and the plane strain state occurs at a much smaller specimen thickness. An optimal combination of high strength, ductility, short- and long-term static crack resistance in air and hydrogen has been achieved in a fine-grained alloy with low carbon and sulfur content. Based on the results of long-term static crack resistance tests at the predetermined maximum fatigue test duration of 300 h, the invariant characteristics of crack resistance, the threshold values of stress intensity factor in hydrogen, have been determined, which vary from 23 to 48 MPa ∙ m1 / 2 depending on the alloy heat treatment mode.

Numerical study on the symmetric and asymmetric orientation of the crack branching in 2D plate

The phenomenon of crack branching is one of the typical fracture behaviours. The effect of crack branching orientation is investigated in this paper. By considering a static branched crack in a 2D plate under uniaxial traction, the numerical study is carried out for two study cases. The first study case is the symmetric crack branching in which the various crack branching length and orientation have the same value between both crack branching. The second case is the asymmetric case crack branching. In this case, both crack branching length has a particular constant value, Moreover, the orientation of first crack branching is constant and then the second one has various values. The stress intensity factors of the crack tips are calculated for both study cases. It is revealed for the symmetric case; the increasing of the crack branching length will increase the value of stress intensity factors KI for various orientations of crack branching. In contrast, the stress intensity factors KI will tend to decrease along with the increasing of the crack branching orientation. Moreover, the stress intensity factors KI of first crack branching will increase, but the stress intensity factors KI of second crack branching will decrease along with increasing of the second orientation crack branching for the asymmetric case. Furthermore, the direction the stress intensity factors KII will prone to change along with the increasing of the crack branching orientation. The stress intensity factor KII tends to increase along with the increasing of the crack branching orientation as well as the increasing of the crack branching length for the symmetric case. And then the increase of constant angle of first crack branching will increase significantly the stress intensity factors KII of the first crack tip along with the increasing of the second crack branching angle for the asymmetric case.

A Fractal Model of Cracking of Cement Matrix Composites

The modern methods of materials (including cement matrix materials) design and testing impose the application of an approach appropriate to materials engineering. A quantitative description of the association between the properties of these materials and their structure is a necessity. What remains the scientific aim, however, is the clarification and description of the occurring phenomena by means of models mapping their actual behavior in the closest way possible. The article presents a cracking fractal model based on tests on the morphology of concrete fracture surfaces. The recorded fractal nature of the cracking of cement matrix materials enabled fractal geometry in the model development to be applied. Owing to the application of statistical analysis, together with an extensive base of data on the profile lines separated out of the real fracture surfaces of concrete, it was possible to develop a cracking fractal model. Not only does this model satisfy the condition of the equality of the fractal dimension of the real and model profile lines, it also offers the possibility of introducing an order to the apparently chaotic phenomena, such as the cracking process. An advantage and novelty of the model is that unlike the other authors’ proposals, there is a possibility of reaching an infinitely large number of solutions for model profile lines, which approximates the model to the real-life scenario. The results of fractal tests were supplemented with strength measurements, identifying concrete’s compressive and fracture toughness (determining the critical stress intensity factor KIcS). A connection between the fractal dimension and the investigated properties of concrete was demonstrated. A higher fractal dimension was observed in the profile lines separated out of the fracture surfaces of concretes of higher water–cement ratio. The advantages of the model include the simplicity and applicability in model studies on other materials of the cement matrix.

An optical method for measuring mixed-mode stress intensity factors for an arbitrarily oriented crack in cylindrical shells

This paper deals with the measurement of mixed-mode stress intensity factors for an arbitrarily oriented crack in cylindrical shells using an optical method based on a new theory of caustics. Completely analytical expressions are derived for caustic curves as well as for initial curves around the tip of an arbitrarily oriented crack in a cylindrical shell under mixed-mode conditions. The effects of mixed-mode condition, radius of curvature, shell thickness and crack angle on the caustic pattern are investigated, respectively. New procedures for the extraction of stress intensity factors KI and KII are presented using the characteristic dimensions of caustic patterns. A series of uniaxial tensile tests are performed on cylindrical shells containing an edge crack which is inclined to the axis of load by a different angle. The mixed-mode stress intensity factors obtained from the method of caustics developed here show a good agreement with previous theories and finite element results under K-dominant assumption.

On the stress field ahead of a stationary crack tip during the transition from primary to secondary creep

Despite the rich body of work on crack-tip asymptotics to date, the characterization of cracks in creeping solids remains an open problem. The purpose of this paper is to quantify the influence of primary creep on the near crack-tip stress field. We do this by simulating a classical compact tension test using a unified creep-plasticity model due to Robinson, Pugh, and Corum. This model accounts for the transition between primary and secondary creep organically through a kinematic hardening variable called the “internal flow stress” (which is related to the dislocation density of the material), and reduces to classical, power-law creep when the flow stress is negligible compared to the Cauchy stress. Stamm and Walz have shown that, in the limit of high stresses, the near crack-tip stress field predicted by the Robinson-Pugh-Corum model is well approximated by the so-called RR solution of Riedel and Rice, which was derived for power-law creeping solids. For low stresses, we find that the RR solution only applies when the primary creep response of the specimen is negligible. Indeed, the main contribution of this work is the identification of a dimensionless number Ξ, which characterizes the primary creep response of a compact tension specimen. When Ξ<<1, the specimen exhibits very little primary creep, and consequently, the RR solution is still accurate within a finite region ahead of the crack tip under both small-scale creep and extensive creep conditions. When Ξ>>1, the specimen exhibits significant primary creep, and consequently, the RR solution is not accurate under small-scale creep conditions (although remarkably there does appear to be a region in which the RR solution is still accurate under extensive creep conditions). Our results suggest that the relevant loading parameter is still the familiar stress intensity factor KI under small-scale creep conditions, and the well-known C*-integral under extensive creep conditions, regardless of the primary creep response of the specimen, in agreement with previous work.

Stress intensity factors KI, KII, KIII, Keq, induced at the crack tip of CT specimens subjected to torsional loading

The paper herein presented shows the Stress Intensity Factors (SIF), KI, KII, KIII, and Keq, calculated for Compact Tension (CT) specimens with different thicknesses (B), namely 2.5 mm; 3 mm; 5 mm, 7.5 mm, and 10 mm, that were subjected to three torsional loads (T): 6 N.m; 7.5 N.m; 9 N.m. Fatigue pre-crack subjected to torsional loading was found to be predominantly under Mode-II loading, and a crack branch was observed.The CT specimens, which were analysed using the Finite Element Method (FEM), were then modelled with two cracks that had grown experimentally from a fatigue pre-crack along two directions (+70º and -70º), and for several crack lengths (a/L=0; a/L=0.25; a/L=0.50; a/L=0.75; a/L=1.0). Therefore, equivalent SIF, Keq, were calculated from the numerical results of KI, KII, ans KIII, and a polynomial regression function was determined in function of the thickness of the specimen (B), the crack length (a/L) and the applied torque (T). It was observed that even in the case of a Mode-III loading is applied, Mode I was locally dominant at the branched crack tip, followed by Mode III and Mode II, in that order of relevance. It was also observed that the maximum equivalent SIF occurred at the two outer lateral surfaces of the CT specimens under test, resulting in high crack growth rates in those locations, and minimum at the midplane of the specimen.

A study of the crack initiation angle in the substrate of spur gear teeth subjected to rolling contact fatigue

Fracture failure of engineering structures is caused by cracks that extend beyond a safe size. For modeling the stable fatigue crack propagation it is necessary to determine the angle of crack initiation, i. e. the angle under the crack growth takes place. There are several criteria that try to model this aspect, such as: Sih, MTS, M, T, Ip.The S-criterion (Sih) was used to simulate the fatigue growth of an internal crack situated in the substrate of a certain spur gear, taking into account the rolling contact fatigue. S-criterion states that the direction of crack initiation coincides with the direction of minimum strain energy density along a constant radius around the crack tip. Since the stress intensity factor Ki is negligible (because of the compression stresses in the substrate of the gear tooth), calculations were made for these conditions and it was obtained a constant and unique angle of crack initiation angle 9 ∼ 80°, that is in concordance with the experimental observations. This study serves to determine the fatigue crack initiation angle in a compression stresses field, as well as its use in modeling the propagation of the fatigue cracks.

Stress Concentration at Load-Carrying Fillet Welded Cruciform Joints Subjected to Tensile and Bending Loads

Abstract This article presents numerical finite element method (FEM) analysis of the stress concentration at toes and crack-like faults in load-carrying fillet welded cruciform joints with transversal slits resulting from non-fused root faces. Potential fatigue damage of such joints subjected to cyclic tensile and bending loads appears in the form of fatigue cracks starting from the weld roots or toes. The aim of this article is to find qualitative and quantitative relationships between geometrical parameters of the load-carrying fillet welded cruciform joint subjected to tensile and bending loads and the stress concentration at weld toes and roots. The results of the analysis represented by the stress concentration factors (SCFs) and the stress intensity factors KI and KII are shown in the form of tables, graphs and mathematical formulas, which may be applied for fatigue assessment of such joints.

The edge-notched clamped beam bend specimen as a fracture toughness test geometry

Edge-notched clamped beam bend fracture specimens provide the required geometric stability for controlled crack growth in brittle materials, enabling the measurement of R-curves and cyclic crack growth. In this paper, finite element simulations were carried out on this test geometry to extract the normalized stress intensity factor KI solutions for different useful specimen dimensions, loading tip radius and loads. Based on these results, geometric factors have been proposed that can fit various beam aspect and crack depth ratios. Crack stability analysis is carried out in terms of the R locus for various beam aspect ratios for the clamped beam geometry and compared to other fracture toughness tests. Experimental verification of the same has been carried out at the macro-scale using poly-methyl methacrylate (PMMA) and WC-Co as model materials.

Laser-assisted cyclic chipless splitting for hard-to-cut thick wall tubes and fatigue fracture mechanism analysis

High-quality precision cropping of hard-to-cut thick wall tubes is urgently needed as the first process for precision forming of tubular parts. Due to the deficiencies of large cutting load and waste of chips and coolants in the present cutting methods, a laser-assisted cyclic chipless splitting (LACCS) method is developed, which prefabricates circumferential crack with large stress concentration by laser, and exerts cyclic rotary load at a low amplitude simultaneously to split the tube. The theoretical laser crack depth and critical loads are derivated for fatigue crack propagation and instant rupture, respectively, and an XFEM model based on cohesive damage criterion is established to reveal the fracture mode based on stress intensity factors. Finally, section quality and microfracture mechanism are investigated by experimental tests with different initial crack depths and load control curves. The results show that critical fatigue splitting load and instant rupture load gradually drop with crack depth at a decreasing rate; for crack depth of 0.7 mm, the critical loads are 0.67% and 34.36%, respectively, of that in the traditional cutting method. The type I crack is the primary fracture mode in this LACCS process, and the stress intensity factor KI varies as a cosine curve with peak amplitude of 436.09 MPa(m)1/2. Step-reduction frequency load can smoothly transite the crack propagation to final rupture, and obtains high-quality sections in 16–32 s, with outer roundness error of 0.6%, flatness error of 0.2–0.3 mm and final rupture area of 0.25–1.19 mm2. The fractographies typically show laser affected zone, cracks propagation zone and final rupture zone. Micro-cracks initiate from the tangency points on the laser notch curve with maximal stress change rate, and the ductile striations propagate with growth rate of 3.3–5.1 μm/cycle. Final rupture zone forms under shear stress, featured by quasi-parabolic dimples involving microvoid coalescence.

Two- and Three-Dimensional Failure Criteria for Laminate Composites

Abstract Several two- and three-dimensional mixed-mode interface failure criteria are proposed for predicting delamination failure in multidirectional, laminate composites. The proposed criteria, based on the stress intensity factors K1, K2, and KIII, as well as the critical interface energy release rate Gic and phase angles ψ and ϕ, are examined using results obtained from Brazilian disk mixed-mode fracture toughness tests. Two material systems are considered. The first contains a delamination along an interface between a unidirectional fabric and a plain woven fabric. The second is composed of a plain woven fabric with fibers oriented in different directions in succeeding plies. The former was manufactured by means of a wet-layup and the latter is a prepreg. Finally, a statistical analysis is carried out to obtain a failure curve or surface with a 10% probability of unexpected failure and a 95% confidence. These curves or surfaces may be used to predict failure of structures containing these laminates and to assist in composite design.

Optimization of Composite Process Parameters on Fracture Toughness of Glass Fiber Reinforced Plastics

The objective of the work was to investigate statistical analysis of fracture toughness of the glass fiber reinforced composites at different stacking sequences, strain rate and crack length. The glass reinforced Vinylester composites prepared by hand lay-up technique with various stacking sequences such as 0/90, 45/-45 and chopped strand orientations. 3-point bending for fracture toughness test for various notch depth ratio’s as per linear elastic fracture mechanics concept was conducted. Further the initial notch depth method was adopted to find the critical stress intensity factor KIC for the given notch depth ratio. Design of experiment using the Taguchi L9 array was formulated to understand the influence of parameters on fracture toughness. ANOVA was performed to find out the influencing weightage factor for fracture toughness. Regression analysis was used to develop a mathematical model that gave the contribution of individual parameters on responses. The fracture surface was investigated using scanning electron microscopy (SEM).The DOE response surface methodology showed the stacking sequence of [45/-45/0/90/Chopped]3s, with strain rate of 0.5 mm/min and without notch having the highest fracture toughness of 81.36 Mpa . ANOVA was carried out to know the statistical significance of factors influencing fracture toughness, Results showed that notch depth ratio was the most influencing factor with 68.67 % and stacking sequence with 24%. Accuracy of developed regression model was 90.61 % (R2), which indicating the confidence level of regression.