Equivalent Stress Intensity Factor Research Articles

Fracture analysis of load-carrying cruciform welded joint with a surface crack at weld toe

The load-carrying cruciform welded joint usually fails in the weld root or the weld toe. Determining the failure location in terms of the stress intensity factor (SIF) of the crack at the weld root and the weld toe is an alternative. Various SIF equations have been proposed and incorporated in the British Standard (BS) 7910:2013, including the equations for the welded cruciform joint with a weld toe crack. However, the SIF equations for the weld toe crack are based on 2-D finite element (FE) analysis, which predicts an over-conservative result. In fact, a crack at the weld toe often resembles a semi-elliptical shape. Hence, it is necessary to propose new SIF equations for the load-carrying cruciform welded joint containing a weld toe crack by 3-D FE analysis. The new equations are built up based on multiple regression analysis and the goodness of fit is confirmed via error distribution and statistical analyses by comparing with the FE results. The proposed SIF equations have a wide applicability in the failure analysis of the load-carrying cruciform welded joint.

Crack tip fields and fracture resistance parameters based on strain gradient plasticity

The crack tip mechanics of strain gradient plasticity solids is investigated analytically and numerically. A first-order mechanism-based strain gradient (MSG) plasticity theory based on Taylor’s dislocation model is adopted and implemented in the commercial finite element package ANSYS by means of a user subroutine. Two boundary value problems are considered, a single edge tension specimen and a biaxially loaded plate. First, crack tip fields are characterized. Strain gradient effects associated with dislocation hardening mechanisms elevate crack tip stresses relative to conventional plasticity. A parametric study is conducted and differences with conventional plasticity predictions are quantified. Moreover, the asymptotic nature of the crack tip solution is investigated. The numerical results reveal that the singularity order predicted by the first-order MSG theory is equal or higher to that of linear elastic solids. Also, the crack tip field appears not to have a separable solution. Moreover, contrarily to what has been shown in the higher order version of MSG plasticity, the singularity order exhibits sensitivity to the plastic material properties. Secondly, analytical and numerical approaches are employed to formulate novel amplitude factors for strain gradient plasticity. A generalized J-integral is derived and used to characterize a nonlinear amplitude factor. A closed-form equation for the analytical stress intensity factor is obtained. Amplitude factors are also derived by decomposing the numerical solution for the crack tip stress field. Nonlinear amplitude factor solutions are determined across a wide range of values for the material length scale l and the strain hardening exponent N. The domains of strain gradient relevance are identified, setting the basis for the application of first-order MSG plasticity for fracture and damage assessment.

Fatigue crack growth behavior of rib-to-deck double-sided welded joints of orthotropic steel decks

Innovative double-sided welding is expected to improve the fatigue resistance of rib-to-deck welded joints of orthotropic steel decks (OSDs). Welding crack-like defects are the crucial issue affecting the fatigue performance of rib-to-deck double-sided welded joints. This study presents a numerical simulation of three-dimensional (3D) mixed mode fatigue crack growth behavior of rib-to-deck double-sided welded joints of OSDs. Maximum tensile stress theory and equivalent stress intensity factor (SIF) were used to simulate mixed mode fatigue cracks growth. The Paris law model was employed to predict the fatigue life. Fatigue cracks of rib-to-deck double-sided welded joints were characterized by the presence of mixed mode cracks of modes I (open), mode II (shear), and mode III (tear), which was dominated by mode I. The equivalent SIF was found to be complex at the growth stage with the maximum value at the two ends of the crack front and the minimum value at the midpoint of the crack front. The crack shape became flatter in the later phase of the crack growth. The fatigue crack surface underwent deflections during crack growth, making the final crack shape exhibiting the characteristic of a spatial curved surface. The initial crack geometry showed a significant impact on the fatigue life.

Adaptive Finite Element Prediction of Fatigue Life and Crack Path in 2D Structural Components

The existence of a hole near a growing fatigue crack can cause the crack trajectory to deviate. Unless the hole is too close to the crack, the crack is arrested at the edge of the hole and does not progress further. The purpose of this paper was to predict the crack propagation and lifetime of two-dimension geometries for linear elastic materials in mixed-mode loading using a finite element source code program written in Visual Fortran language. The finite element mesh is generated using the advancing front method. The onset criterion of crack propagation was based on the equivalent stress intensity factor which provides the most important parameter that must be accurately estimated for the mixed-mode loading condition. The maximum circumferential stress theory was used as a direction criterion. The modified compact tension (MCTS) was studied to demonstrate the influence of the hole’s presence on the direction of crack growth and fatigue life for different configurations. The Paris’ law model has been employed to evaluate the mixed-mode fatigue life for MCTS in different configurations under the linear elastic fracture mechanics (LEFMs) assumption. The framework involves a progressive crack extension study of stress intensity factors (SIFs), crack growth direction, and fatigue life estimation. The results show that the fatigue growth was attracted to the hole either changes its direction to reach the hole or floats by the hole and grows as the hole is missed. The results of the study agree with several crack propagation experiments in the literature revealing similar crack propagation trajectory observations.

Numerical solutions of hypersingular integral equations for stress intensity factors of planar embedded interface cracks and their correlations with bimaterial parameters

This paper studies the stress intensity factors and their correlations with bimaterial parameters for the interface planar cracks by hypersingular integral equations. A new bimaterial parameter γ is defined, and the correlations of the stress intensity factors of interface planar crack with two parameters ε and γ are proved. The relative displacement fundamental function is proposed based on the crack's peripheral equation, thus one kind of element with coupled oscillatory characteristic of mode-1 and mode-2 is established for the interface planar crack. For the interface elliptical cracks with b/a = 0.2, 0.4, 0.6, 0.8, 1.0, the stress intensity factors along the crack front are calculated by solving the hypersingular integral equations. Comparison with the existing exact solutions show that the numerical results have a high accuracy. For the interface planar cracks under tensile load, there exist K1, K2 and K3 at the same time. The numerical results show that K1 is very weakly related to ε and γ, K2 strongly to ε and weakly to γ, and K3 shows a significant correlation with both parameters ε and γ. K3 is much smaller than K1 and K2 and can be ignored in fracture analysis of problems with remote mode-1 loading.

Methodical approach for studying kinetics of short and long fatigue cracks growth for irradiated reactor materials. Part 2. Сonstruction of fatique propagation rate diagram on the basis of test of precracked charpy specimens

The finite element technique has been used for estimating the stress intensity factors (SIF) for short cracks emanating from a notch of single-edge bend specimen (SE(B)) and also weight function for this type of the specimen have been determined. On the basis of the received results the uniform equation for calculations SIF for short and long cracks in a specimen such as SEB (at h/W = 0.3) has been offered. The technique of construction of full kinetic diagrams of growth of the short and long fatigue cracks, initiated from the notch, is developed and approved. Full kinetic diagrams of growth of fatigue cracks (short and long) in steel Х18Н10Т and in weld metal in initial and irradiated (up to 40 dpa) conditions were built.

Theoretical model of caustics method for the interfacial cracks

As a non-contact optical experimental method, caustic method is commonly employed in measuring stress intensity factor at the crack tips of different materials. Caustics theory is commonly used for solving stress intensity factor at crack tips in homogeneous isotropic materials, but it lacks the required accuracy for solving stress intensity factor in interfacial cracks in dissimilar materials. In this paper, we have deduced the theoretical equation of stress intensity factor at interfacial crack tips the orthotropic bi-materials and evaluated the effects of different crack propagation speeds, orthotropic bi-materials and other parameters on the initial curves of focal line and the shape of caustics. In addition, dynamic caustic experiments on composite/epoxy bi-materials under low velocity-impact loadings were performed and the evolution of dynamic interfacial cracks was captured by high-speed cameras which showed good agreements with theoretical results. Research results confirmed the usefulness of the application of caustic method in dissimilar isotropic and orthotropic materials, isotropic-orthotropic bi-materials and homogeneous isotropic and orthotropic materials under subsonic crack propagation velocities.

Elastoplastic 3D analyses of plastic zone size dependencies on load-to-yield strength and on crack size-to-width ratios under mixed mode I/II

A pure mode-I approach cannot properly analyze many important practical problems that involve combined mode I and II loadings, which in particular may not be sufficient to estimate crack paths and fracture toughness in such cases. Multiaxial crack tip conditions characterized by a crack inclination angle β in a modified mixed-mode single edge tension SE(T) specimen are used to consider mixed-mode effects on the shapes and volumes of the plastic zones (pz) that form ahead of crack tips, as well as on the plastic work Upl dissipated inside them. A methodology is proposed to evaluate pz volumes Vpz based on a sub-modeling FE analysis that uses the influence volume around a plastified Gauss integration point. For a given Equivalent Stress Intensity Factor Keq, both Vpz and Upl are evaluated for different nominal stress to yield strength ratios σn/SY and several combinations of geometric parameters β, W/B and a/W, where a is the crack size, W is the cracked specimen width, and B is its thickness. Before performing all these analyses, compatibility and convergence studies are carried out to validate the submodels used in such analyses.

Fatigue strength evaluation of self-piercing riveted joints of AZ31 Mg alloy and cold-rolled steel sheets

Abstract The application of magnesium alloys to automobiles is increasing due to their superior specific strength and specific stiffness. In this study, an upper sheet of AZ31 magnesium alloy and a lower sheet of cold-rolled steel were joined by self-piercing riveting (SPR), a method commonly used to join automotive panels. A cross-shaped specimen was fabricated with a punching force of 35 kN, which exhibited the best joint strength for the SPR joint specimen geometry. Monotonic and fatigue strengths were evaluated using cross-shaped specimens at loading angles of 0°, 45°, and 90°. The load amplitude corresponding to the fatigue endurance limit was assumed to be at 106 cycles, and the fatigue ratios (= fatigue endurance limit/static strength) at the loading angles of 0°, 45°, and 90° are 22%, 13%, and 9%, respectively. For all three loading angle specimens, fatigue cracks initiated at the triple point where the rivet shank, the upper sheet and the lower sheet are in contact with each other, with the cracks propagating through the thickness of the upper sheet and ultimately leading to fracture. The fatigue lifetimes were evaluated through the von-Mises stress, maximum principal stress, and equivalent stress intensity factor. It was found that the fatigue lifetimes could be evaluated most appropriately through the maximum principal stress.

Fatigue life prediction of spot-welded joints with a notch stress approach

Spot-welded joints are widely used in the construction of vehicle structures and frequently become critical locations for fatigue failure. Hence, it is essential to have reliable fatigue life prediction method for the spot-welded joints during vehicle structure design. In this paper, a new notch stress approach is developed for fatigue life prediction of the spot-welded joints. Currently, structural stress methods are widely used in automotive industry for fatigue life prediction of spot-welded joints. However, these methods are not well considering local geometry information. This paper introduces a notch stress based method to overcome the limitation of the structural stress methods. In the notch stress method, stress concentration factors for spot-welded joints are calculated from stress intensity factor equations. Then, the notch stress method is validated with fatigue test results of lap-shear and coach peel specimens.

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.

Numerical Simulation of Mixed‐Mode Fatigue Crack Growth for Compact Tension Shear Specimen

This work concentrates on the fracture behaviour of the compact tension specimen under mixed‐mode loading, and numerical investigation using ANSYS Mechanical APDL 19.2 finite element program with different modes of mix angles is carried out. The prediction of mixed‐mode fatigue life under constant amplitude fatigue loading for the compact tension shear specimen (CTS) is employed using Paris’ law model for two different loading angles with agreement to the experimental results. The predicted values of ΔKeq were compared with the experimental and analytical data for various models. Depending on the analysis, the findings of the present study show consistency with the results achieved with similar models of predicting the equivalent stress intensity factor. In addition, the direction of crack growth derived from the analysis was observed to follow the same trend of the literature experimental results.

Subsurface Crack Propagation from Internal Defect in Rolling Contact Fatigue of Railway Wheel Steel

A rolling contact fatigue failure is one of the main fatigue damages in railway wheels due to cyclic rolling contact with rails. This fatigue failure caused by internal defects such as nonmetallic inclusions or voids might occur in heavy haul freight car wheels. Subsurface crack propagation behaviors from the internal defects are evaluated by twin disc type rolling contact fatigue tests using test specimens with artificial defects and by finite element analyses simulating the rolling contact fatigue tests. The subsurface cracks are more likely to propagate in the test specimens with larger artificial defects. In addition, the cracks initiating from the trailing side of defects propagate faster than those from the leading side. Shear mode equivalent stress intensity factors obtained from the finite element analyses correspond well to the results of rolling contact fatigue tests. The test specimen models with larger defect have larger equivalent stress intensity factor ranges than the test specimen model with smaller defect in both leading and trailing side. The results of finite element analyses also suggest that the crack propagations are affected by the deformation of artificial defects and this leads to have higher resistance to crack propagation in the test specimens with smaller internal defects.

Mixed mode fatigue crack growth studies in AISI 316 stainless steel

Damage tolerance assessment requires the accurate prediction of fatigue crack growth lives. Numerical simulation techniques using mixed mode Paris' law and various equivalent stress intensity factor models (ΔKeq) are widely employed for fatigue life prediction. In the present work, mixed mode (I/II) fatigue crack growth experiments are performed using the compact tension shear specimens made of AISI 316 austenitic stainless steel for various loading angles. Finite element fatigue crack growth simulations are carried out, and the effect of ΔKeq model in fatigue life prediction is studied. To achieve this, a three parameter double exponential type best fit is proposed for fitting the experimental mixed mode crack length vs fatigue life. The performance and capability of various selected models are assessed by comparing the predicted life with the experimental results. Fractographic studies at different stages of crack propagation for different loading angles are also presented to aid the above assessments. Based on the overall consistent performance, Irwin's and Tanaka models are predicting life close to the experimental data and Richard's and Yan's models provide conservative solutions.

The influence of heat treatment on the behavior of fatigue crack growth in welded joints made of S355 under bending loading

The work concerns on the results of the tests of the growth of the fatigue crack experiment. All specimens were subjected to bending at constant load using S355 steel. Rectangular cross-section specimens were weakened by external notches and fillet welded joints. The tests were carried out under cyclic bending without and with mean load values. Additionally, the impact of heat treatment on fatigue lifetime was investigated. Crack initiation and propagation stages were observed on the specimens’ surface using a light microscope. This research also shows microstructures with cracks of welded connectors and with changes in the material after heat treatment as well as their effect on the fatigue lifetime of joints. The highest durability was demonstrated by specimens without heat treatment. On the other hand, a similar fatigue crack growth mechanism was observed in different weld types. The numerical analysis also explains similar fatigue crack growth mechanism by equivalent stress intensity factors values. The fatigue life of welded specimens without heat treatment for both stress R-ratios was higher than for specimens after heat treatment.

Mixed Mode I/III fatigue fracture characterization of Polyoxymethylene

The crack growth behaviour of thermoplastic polymers is a relevant topic in current research. While a dominant portion of studies in fracture mechanics investigates Mode I loading situations, very little is done to better understand Mixed Mode crack growth, which can be equally important to accurate live time predictions of polymer parts. In this research, fatigue tests on cylindrically notched specimens were performed in Mixed Mode I/III loading and compared via the so called equivalent stress intensity factor. Under these loading conditions, a significant reduction of the cycles to fracture occurred compared to pure Mode I.

Crack Initiation Criteria and Fracture Simulation for Precracked Sandstones

The friction coefficient, tip curvature, and different-width crack state influence the stress intensity factor (SIF). The maximum circumferential tensile stress (MTS) and minimum strain energy density criterion (S) face challenges in explaining the mode-II fracture propagation of cracks. The maximum radial shear stress (MSS) and modified twin shear stress factor (ITS) criteria are proposed as the brittle mode-II fracture criteria. The experiments and numerical analysis are also performed. The results indicate that the fracture angles of the MSS and ITS were similar and different from the results of MTS and S. The equivalent stress intensity factors (ESIFs) from the mixed mode I-II are proposed to determine the fracture mode. There are different fracture models for different cracks under tensile and compressive stresses. The ratio of the tensile strength to uniaxial compressive strength influenced the fracture angle of ITS. The lateral pressure coefficient (k) had a significant effect on the mode-II fracture angle when the angle between the crack and the vertical direction is less than 40° and the lateral pressure coefficient is more than 0. Because the same fracture mode k (k > 0) can inhibit mode-I fracturing, conversely, it can also promote mode-I fracturing. Experimental results and numerical simulations of fracture propagation under uniaxial compression confirmed that the theoretical results were correct.

Mixed mode fatigue and fracture in planar geometries: Observations on Keq and crack path modelling

AbstractThe mixed mode I‐II fatigue and fracture is briefly reviewed, addressing experimental and numerical modelling aspects, and focusing on planar specimens. One major challenge concerns the determination of equivalent stress intensity factor (Keq) in mixed mode situations. Several approaches were compared through the determination of Keq/KI over a wide range of values of KI/KII or KII/KI. Whereas all different approaches converge to the same value as KI/KII increases, the same does not happen for large KII/KI, where differences between values of Keq persist. In the regions of 0 < KI/KII < 2 and 0 < KII/KI < 2, no stable trend of results can be defined.Experimental fatigue crack growth results are presented for Al alloy AA6082‐T6. Compact tension specimens, modified with holes, and four‐point bending specimens under asymmetrical loading promoting mixed mode situations, were subjected to fatigue crack growth tests, where crack path and crack growth rate were measured. The presentation of the fatigue crack growth data was made using a Paris law based upon Keq. Differences in the Paris law constants were found for the different Keq criteria.Recent developments in numerical techniques, as the implementation of the extended finite element method (XFEM) in finite element software packages allows to determine accurately crack paths in mixed mode fracture. This article highlights concepts for mixed‐mode fatigue and fracture and supporting data, identifying challenges still to be overcome.

Fatigue Crack Growth under Non-Proportional Mixed Mode Loading in Rail and Wheel Steel Part 2: Sequential Mode I and Mode III Loading

Rolling contact fatigue cracks in rail and wheel undergo non-proportional mixed mode I/II/III loading. Fatigue tests were performed to determine the coplanar and branch crack growth rates on these materials. Sequential and overlapping mode I and III loading cycles were applied to single cracks in round bar specimens. Experiments in which this is done have been rarely performed. The fracture surface observations and the finite element analysis results suggested that the growth of long (does not branch but grown stably and straight) coplanar cracks was driven mainly by mode III loading. The cracks tended to branch when increasing the material strength and/or the degree of overlap between the mode I and III loading cycles. The equivalent stress intensity factor range that can consider the crack face contact and successfully regressed the crack growth rate data is proposed for the branch crack. Based on the results obtained in this study, the mechanism of long coplanar shear-mode crack growth turned out to be the same regardless of whether the main driving force is in-plane shear or out-of-plane shear.

Effects of Mixed Mode Loading Conditions on Fatigue Crack Growth Rate

The fatigue crack growth rate is the most important factor in predicting the life of a product when applying the damage tolerance design concept. Studies related to pure mode I for structures under fatigue loading have been actively conducted, while not many studies are conducted on the mixed mode. In this study, therefore, mixed mode fatigue crack growth experiments were designed using the Compact-Tension-Shear (CTS) specimens and the loading devices, proposed by Richard. Furthermore, the finite element analysis was used in determining the stress intensity factors of CTS specimen. As the results, the fatigue crack growth rate using the equivalent stress intensity factors proposed by previous researchers was lower than that of pure mode I at the initial stage of crack growth when the load angle increases.