Comparison of mode I and mode II elastic-plastic fracture toughness for two low alloyed high strength steels

In the present work, mode I and mode II tests were carried out on two low alloyed high strength steels. An asymmetrical four point bend specimen and J _II-integral vs. crack growth resistance curve technique were used for determining the mode II elastic-plastic fracture toughness, J _IIc · J _II-integral expression of the specimen was calibrated by finite element method. The results indicate that the present procedure for determining the J _IIc values is easy to use. Moreover, the mode I fracture toughness J _Ic is very sensitive to the rolling direction of the test steels, but the mode II fracture toughness J _IIc is completely insensitive to the rolling direction of the steels, and the J _IIc /J _Ic ratio is not a constant for the two steels, including the same steel with different orientations. Finally, the difference of the fracture toughness between the mode I and mode II is discussed with consideration of the different fracture mechanisms.     

J integral and COD fracture criteria in 40CrNiMo steel under mixed mode I+II loading

Abstract

By defining the J integral and crack opening displacement (COD) under mixed mode I + II loading, a mixed J integral fracture criterion is proposed and the relationship between the J integral and COD in 40CrNiMo steel is discussed. The mixed J integral J _M and its mode I and II components J _I and J _II were calculated by the finite element method, while the mixed COD and its mode I and II components CTOD and CTSD were measured using a duplicated grid. The critical values J _Mc and COD_c for mixed crack initiation were determined by a resistance curve. The results show that mode II loading lowers both J _Mc and COD_c for 40CrNiMo steel. The variation of J _Mcfrommode I tomode II loading is found to be in accordance with the linked equations J _Mc=J _Ii+J _IIi;(J _Ii/J _Ic)+(J _IIi/J _IIc)=1, where J _Icand J _IIcare the critical J integrals of pure mode I and II cracks,and J _Iiand J _IIiare the mode I and II components of J _Mc at arbitrary mixed K_I/K_II ratio respectively; the J _Mc value for a given K_I/K_II ratio can be obtained if J _Ic and J _IIc are known. Finally, under valid loads, J_M and the mixed COD satisfy the relation J _M=J _I+J _II=dσ₀CTOD+d _sτ₀CTSD. When unified by yield stress σ_y the relation becomes J _M=dσ_yCOD, where d _n, d _s and d are coefficients, and σ₀ and τ₀ are the tensile and shear stress at the crack tip strip respectively. While d _n and d _s vary with K_I/K_II ratio and materials, d was found to have a constant value of about 0.98.     

An insight into mode II fracture toughness testing using SCB specimen

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

The effects of ferrrite grain size on fracture of low carbon steel under mixed modes I and II

In the previous article a new methodology is proposed for the study on fracture criterion for the notched or cracked specimens under mixed Modes I and II. In this methodology, any value of K_II/K_I can be applied to the thin-walled hollow cylindrical specimen with notch or crack, the length of which is perpendicular to the specimen axis. Thus the data can be obtained covering all values of K_II/K_I ranging from ∝ to 0, that is, from mode II to mode I.Using this method, the experimental studies were carried out on the effects of ferrite grain diameter upon the fracture of low carbon steel under mixed Modes I and II. The experimental results were compared with various fracture criteria hitherto proposed in literatures. The fracture criterion experimentally obtained is a function of ferrite grain diameter and the value of K_II/K_I, at fracture increases with increase of ferrite grain diameter. On the other hand, the overall direction of the crack growth obeys approximately maximum stress criterion or energy momentum tensor criterion, independent of ferrite grain diameter. Furthermore, this also shows that the fracture criterion does not reveal directly overall direction of crack growth. These characteristics are quite similar in trend to those of the unnotched specimens.     

Mode II fracture testing method for highly orthotropic materials like wood

In this paper a mode II fracture testing method has been developed for wood from analytical, experimental and numerical investigations. Analytical results obtained by other researchers showed that the specimen geometry and loading type used for the proposed mode II testing method results in only mode II stress intensity and no mode I stress intensity at the crack tip. Experiments have been carried out to determine mode II fracture toughness K _IIC and fracture energy G _IIF from the test data collected from both spruce (pice abies) and poplar (populus nigra) specimens. It was found that there existed a very good relation between fracture toughness K_IIC and fracture energy G _IIF when the influence of orthotropic stiffness E _II ^* in mode II was taken into account. It verified that for this mode II testing method the formula of LEFM can be employed for calculating mode II fracture toughness even for highly orthotropic materials like wood. In the numerical studies for the tested spruce specimen, the crack propagation process, stress and strain fields in front of crack tips and the stress distributions along the ligament have been investigated in detail. It can be seen that the simulated crack propagating process along the ligament is a typical shear cracking pattern and the development of cracks along the ligament is due to shear stress concentrations at the crack tips of the specimen. It has been shown that this mode II fracture testing method is suitable for measuring mode II fracture toughness K _IIC for highly orthotropic materials like wood.     

Measurement of mode I and mode II rock dynamic fracture toughness with cracked straight through flattened Brazilian disc impacted by split Hopkinson pressure bar

In order to find an effective and convincing method to measure rock dynamic fracture toughness for mode I and mode II, cracked straight through flattened Brazilian disc specimens of marble, which were geometrically similar for three size, were diametrically impacted by split Hopkinson pressure bar on the flat end of the specimen with three load angle respectively. History of stress intensity factors (K_I(t) for opening mode I, and K_II(t) for sliding mode II), mode mixture ratio (K_I(t)/K_II(t)), as well as mode I and mode II dynamic fracture toughness at crack initiation (K_Id and K_IId) were determined with the experimental–numerical method. It is found that there is a unique size effect for dynamic fracture test with the specimens, the mode mixture ratio is not solely determined by load angle (the angle between load direction and crack line) as in the static loading; the pure mode II load angle is 19° for the ?50 mm specimen, however it is 10° for the ?130 mm and ?200 mm specimens; the mode II load angle decreases with increment of specimen size. Realization of pure mode II is justified by the mode mixture ratio approaching zero, it can be realized under certain load angle and loading rate for the specimen of specified size. K_IId is generally greater than K_Id. Both K_Id and K_IId increase with increment of specimen size, and this trend for K_IId is more remarkable than that for K_Id.     

On the applicability of linear elastic fracture mechanics to environmental stress cracking of low-density polyethylene

The primary aim of this work was to re-examine the range of applicability of linear elastic fracture mechanics (LEFM) to environmental stress cracking of low-density polyethylene. By use of a number of specimen types and a range of specimen dimensions and loads it is shown that theK _I-c relationship is unique only at lowK _Is. The material studied showed a region of constant crack velocity which was not caused by plasticity effects or the failure of LEFM. However, crack arrest, which occurred at highK _Is or loads, was shown to be caused by ductile yielding causing the crack to blunt.     

Experimental and numerical investigation of cracked chevron notched Brazilian disc specimen for fracture toughness testing of rock

The cracked chevron notched Brazilian disc (CCNBD) specimen has been suggested by the International Society for Rock Mechanics to quantify mode I fracture toughness (K_Ic) of rock, and it has also been applied to mode II fracture toughness (K_IIc) testing in some research on the basis of some assumptions about the crack growth process in the specimen. However, the K_Ic value measured using the CCNBD specimen is usually conservative, and the assumptions made in the mode II test are rarely assessed. In this study, both laboratory experiments and numerical modeling are performed to study the modes I and II CCNBD tests, and an acoustic emission technique is used to monitor the fracture processes of the specimens. A large fracture process zone and a length of subcritical crack growth are found to be key factors affecting the K_Ic measurement using the CCNBD specimen. For the mode II CCNBD test, the crack growth process is actually quite different from the assumptions often made for determining the fracture toughness. The experimental and numerical results call for more attention on the realistic crack growth processes in rock fracture toughness specimens.     

Fracture characteristics of cement-stabilized soils

Fracture characteristics of cement-stabilized soil under Mode I (tensile) and Mode II (in-plane shear) were investigated on a series of cube specimens. The linear elastic fracture mechanics approach was applied to study the stress distribution in the specimens and also to determine the constitutive equations for fracture parametersK _I andK _II. The experimental studies were carried out on a range of 100 mm soil-cement cube specimens modified for fracture testing by inserting a series of slots. It was shown that results predicted by numerical models were in acceptable agreement with the experimental observations. The fracture parameterK _I was found to be in the range 0.11–0.17 MN m^−3/2 and the parameterK _II in the range 0.31–0.45 MN m^−3/2. This result indicated that the soil-cement exhibited a greater resistance to shear fracture than was expected.     

Fracture assessment of inclined U-notches made of aluminum 2014-T6 under prevalent Mode II loading by means of J-integral

In this paper, the J-integral has been evaluated for specimens with inclined U-notches loaded under a prevalent Mode II (i.e. K_II/K_I ratio greater than 1). Finite element analyses using ABAQUS software have been applied for evaluation of the J-integral. J = J_cr criterion has been used to predict the critical fracture load. The value of J_cr has been determined by means of some useful formulas available in the literature. Some specimens have been produced by aluminum 2014-T6 with inclined U-notches. The aim of selecting aluminum 2014-T6 is that this material has several applications in aerospace industries such as in aircraft for fittings and wheels, as well as applications in machinery, military and weapons industries. The produced specimens have been tested under prevalent Mode II loading. The results of the critical fracture load predicted numerically are in good agreement with the results obtained experimentally for Al2014-T6.     

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

The 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 (K_eq) in mixed mode situations. Several approaches were compared through the determination of K_eq/K_I over a wide range of values of K_I/K_II or K_II/K_I. Whereas all different approaches converge to the same value as K_I/K_II increases, the same does not happen for large K_II/K_I, where differences between values of K_eq persist. In the regions of 0 < K_I/K_II < 2 and 0 < K_II/K_I < 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 K_eq. Differences in the Paris law constants were found for the different K_eq 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 ferritic-pearlitic steel

Mode II fatigue crack growth tests as well as tests in sequential mode I and then mode II were performed on ferritic‐pearlitic steel. For ΔK_II ranging from 7 to , bifurcation occurs after 12–450 μm of coplanar growth at a decreasing speed. By contrast, hundreds of micrometres of constant speed coplanar growth were obtained under sequential mode I and then mode II loading, for and ΔK_I ranging from 0.25 to 1.0 ΔK_II . The crack growth rate is a simple sum of the contributions of each mode for ΔK_I= 0.25 ΔK_II but above this value a synergetic effect is found. The mechanism of this fast‐propagation mode is discussed in the light of strain range maps ahead of the crack tip obtained by digital SEM image correlation and elastic–plastic finite element calculations. The stability of the crack path according to the maximum growth rate criterion is demonstrated.     

DAMAGE MECHANICS APPROACH TO REMOVE THE CONSTRAINT DEPENDENCE OF ELASTIC–PLASTIC FRACTURE TOUGHNESS

It is now generally agreed that the applicability of a one-parameter J-based ductile fracture approach is limited to so-called high constraint crack geometries, and that the elastic-plastic fracture toughness J_1c, is not a material constant but strongly specimen geometry constraint-dependent. In this paper, the constraint effect on elastic-plastic fracture toughness is investigated by use of a continuum damage mechanics approach. Based on a new local damage theory for ductile fracture(proposed by the author) which has a clear physical meaning and can describe both deformation and constraint effects on ductile fracture, a relationship is described between the conventional elastic-plastic fracture toughness, J_1c, and crack tip constraint, characterized by crack tip stress triaxiality T. Then, a new parameter J_dc (and associated criterion, J_d=J_dc) for ductile fracture is proposed. Experiments show that toughness variation with specimen geometry constraint changes can effectively be removed by use of the constraint correction procedure proposed in this paper, and that the new parameter J_dc is a material constant independent of specimen geometry (constraint). This parameter can serve as a new parameter to differentiate the elastic-plastic fracture toughness of engineering materials, which provides a new approach for fracture assessments of structures. It is not necessary to determine which laboratory specimen matches the structural constraint; rather, any specimen geometry can be tested to measure the size-independent fracture toughness J_dc. The potential advantage is clear and the results are very encouraging.     

Fracture toughness evaluation for short glass fibre reinforced composites

Valid plane-stress fracture toughness evaluation of short fibre reinforced composites relies essentially on the successful separation of the energy absorbed in the localized crack-tip region out of the total energy absorbed by the cracked material body at large. Three different experimental techniques, all stemming from the energetic interpretation of theJ integral, are utilized and their relative merits in the characterization of fracture initiation in short glass fibre reinforced injection-moulded nylon 6.6 examined. Various theoretical aspects concerning these experimental methods are outlined. The rationale behind using a single-edge-notched tension type specimen for theJ _c test is presented. TheJ _c value obtained from the compliance calibration method and the quasistatic energy method agree closely and can be considered to be independent of pre-crack length and specimen geometry when the pre-crack length to specimen width ratio (a/w) is larger than 0.45. The extrapolation method fails nevertheless to yield a physically consistentJ _c value, possibly due to its questionable theoretical representation. As no constraint on boundary conditions is necessitated during the course of crack extension, the quasistatic energy is physically more appealing.     

Elasto-plastic analysis of a mode II fracture specimen

An elasto-plastic analysis of a compact mode II fracture specimen is performed. Both an approximate approach with rigid plastic material and a more exact elasto-plastic finite element calculation are carried out. From this analysis, an -factor is determined relating the J-integral to the internal energy measured along the specimen crack faces. It is shown through the finite element computation that it is justifiable to define an -factor. With this result, it is now possible to perform tests on aluminium specimens so as to determine J _IIc.     

Evaluation of the ISO <Emphasis Type="Italic">J</Emphasis> initiation procedure using the EURO fracture toughness data set

The multiple specimen J _0.2/BL initiation fracture toughness test procedure from the ISO standard, ISO 12135:2002, is evaluated using the EURO fracture toughness data set. This standard is also compared with the ASTM standard, ASTM E 1820, multiple specimen J _Ic procedure. The EURO round robin data set was generated to evaluate the transition fracture toughness methods for steels. However, many of the tests resulted in ductile fracture behavior giving final J versus ductile crack extension points. This is the information that is measured in a multiple specimen J initiation fracture toughness test. The data set has more than 300 individual points of J versus crack extension with four different specimen sizes. It may be the largest data set of that type produced for one material. Therefore, its use to determine J initiation values can provide an important evaluation of the standard procedures. The results showed that a J _0.2/BL value could be determined from the ISO standard for three of the four specimen sizes, the smallest size did not meet the specimen size requirement on J. The construction line slopes in this method are very steep compared with the ASTM construction line slopes. This resulted in low J initiation values, about a factor of two lower than the one from the ASTM method. Of the various criteria imposed to determine a valid J _0.2/BL value, the one limiting the maximum J value was the most questionable. It had an effect of eliminating small specimen data that was identical to acceptable large specimen data.     

Mixed-mode fatigue crack growth behaviour in aluminium alloy

Fatigue crack propagation tests in compact mixed-mode specimens were carried out for several stress intensity ratios of mode I and mode II, K_I/K_II, in AlMgSi1-T6 aluminium alloy with 3 mm thickness. The tests were performed in a standard servo-hydraulic machine. A linkage system was developed in order to permit the variation of the K_I/K_II ratio by changing the loading angle. Crack closure loads were obtained through the compliance technique. A finite element analysis was also done in order to obtain the K_I and K_II values for the different loading angles. Crack closure increases under mixed-mode loading conditions in comparison to mode-I loading due the friction between the crack tip surfaces. Moreover, the crack closure level increases with the K_I/K_II ratio decrease. Correlations of the equivalent values of the effective stress intensity factor with the crack growth rates are also performed. Finally, an elastic–plastic finite element analysis was performed to obtain the plastic zones sizes and shapes and model the effect of mixed-mode loading on crack closure.     

A survey of failure criteria and parameters in mixed-mode fatigue crack growth

From the present survey of the mixed-mode crack growth criteria based on the fracture toughness K _Ic (critical J-integral), it follows that this concept is very extensively and variously used by different authors. The criteria discussed in the work are based on the parameters K, δ, W, and J. The most extensively applied models include the mixed mode I + II described by the stress intensity factor K. The criteria presented in the work are based on the factors affecting the fatigue crack growth during testing, namely stress, crack-tip displacement, or energy dissipation. In the case of mixed-mode cracking, special attention should be paid to the energy approach (application of the J-integral and strain energy density), which seems to be very promising for elastoplastic materials. Under mixed-mode cracking, two things should be taken into account: the rate and direction of fatigue-crack growth. Moreover, the nonproportional loading, crack closure, or overloads strongly affect the process of fatigue crack growth in the case of mixed-mode cracking.     

A fracture mechanics analysis on the fatigue behaviour of cruciform joints of duplex stainless steel

The paper presents the results of an experimental and numerical study on the fatigue behaviour of cruciform load carrying joints made from the duplex stainless steel and failing from the weld root through the weld metal. Fatigue crack growth (FCG) data, obtained in specimens of the weld metal, are presented, as well as threshold data, both obtained for R= 0 and 0.5. The influence of stress ratio is discussed, and the FCGR results are compared with data for low carbon structural steels. S–N data were obtained in the joints, both for R= 0.05 and 0.5, and the fatigue cracking mechanisms were analysed in detail with the SEM. It was found that the cracks propagated very early in the lifetime of the joints, under mixed mode conditions (I + II), but the mode I component was found to be predominant over mode II. The geometries of the cracks were defined in detail from measurements taken in the fracture surfaces. A 2D FE analysis was carried out for the mixed mode inclined cracks obtained at the weld root, and the J‐integral formulations were obtained as a function of crack length and crack propagation angle. The values of the crack propagation angle, θ_i, were obtained for the J_max conditions, and it was found that, in the fatigue tests, the cracks propagated in directions very close to the predicted directions of maximum J. K_I and K_II formulations were obtained, and the K_I data were compared with the formulations given in the PD6493 (BS7910) document, and some differences were found. A more general formulation for K under mixed mode conditions was derived. The derived K solutions were applied to predict the fatigue lives of the joints under crack propagation, and an extremely good agreement was found with the experimental results obtained in the fatigue tests.     

Fatigue de-bond growth in adhesively bonded single lap joints

The fatigue de-bond growth studies have been conducted on adhesively bonded lap joint specimens between aluminium and aluminium with Redux-319A adhesive with a pre-defined crack of 3 mm at the bond end. The correlations between fracture parameters and the de-bond growth data are established using both numerical and experimental techniques. In the numerical method, geometrically non-linear finite element analyses were carried out on adhesively bonded joint specimen for various de-bond lengths measured from the lap end along the mid-bond line of the adhesive. The finite element results were post processed to estimate the SERR components G _I and G _II using the Modified Virtual Crack Closure Integral (MVCCI) procedure. In experimental work, specimens were fabricated and fatigue de-bond growth tests were conducted at a stress ratio R = − 1. The results obtained from both numerical analyses and testing have been used to generate de-bond growth curve and establish de-bond growth law in the Paris regime for such joints. The de-bond growth rate is primarily function of mode-I SERR component G _I since the rate of growth in shear mode is relatively small. The value of Paris exponent m is found to be 6.55. The high value of de-bond growth exponent in Paris regime is expected, since the adhesive is less ductile than conventional metallic materials. This study is important for estimating the life of adhesively bonded joints under both constant and variable amplitude fatigue loads.