Study of the relationship between J-integral and COD parameters under mixed mode I + II loading in aluminum alloy Ly 12

In this paper, the relationship between the J-integral and COD under mixed mode I+II loading was proposed and investigated. The J-integral was calculated by the Finite Element Method, and COD was defined by Rice`s model and measured by a duplicating method in an aluminum alloy Ly12. The critical values of the J-integral and COD for a stable mixed crack initiation were also determined by a resistance curve. It shows that: (1) the mixed J-integral, J _M, and the mixed COD satisfy the relations of J _M=dn₀CTOD+ds₀CTSD and J _M=d_yieldCOD, where dn, ds and d are coefficients; CTOD and CTSD are the mode I and mode II components of COD, respectively; ₀ and ₀ are the tensile and shear stresses at the crack tip strip, respectively, and (2) the initiation values of the J-integral and COD of mixed stable crack growth increase with an increasing mode II component, the J _IIC value is 2 times greater than that of J _IC, and the COD_i for a pure mode II crack is 6 times greater than that of COD_i for a pure mode I crack.     

Two parameter approach for elastic-plastic fracture of short cracked specimens under mixed mode loading

For mode-I loading, in order to describe the near-tip stress field in a specimen under large scaled yielding, two parameter approaches such as J-T, J-Q and J-A₂ theories have been developed and proved well for their validity and limit. In this work elastic-plastic finite element analysis were performed to investigate the effects of mode mixity and T-stress upon near-tip stress distribution for a small-scale-yield model with the modified boundary layer and CTS (Compact Tension-Shear) configuration under large-scale-yield state. As the results, some peculiar characteristics were found as follows; As the mode mixity increases, normal stresses _rr and near the crack tip in the small-scale-yield model get significantly affected by the positive T-stress as well as the negative T-stress, while the shear stress _r is little affected by T-stress. Also, the near-tip stress distribution of short cracked CTS specimens under the large-scale-yield state agree fairly well with that of the small-scale-yield model with an appropriate positive T-stress. The two parameters approach with J-integral and T-stress seems to be a good tool for describing the near-tip stress field under a mixed mode loading and large-scale-yield state.     

A criterion for brittle fracture in U-notched components under mixed mode loading

A failure criterion is proposed for brittle fracture in U-notched components under mixed-mode static loading. The criterion, called UMTS, is developed based on the maximum tangential stress criterion and also a criterion proposed in the past for mode I failure of rounded V-shaped notches [Gomez FJ, Elices M. A fracture criterion for blunted V-notched samples. Int J Fracture 2004;127:239-64]. Using the UMTS criterion, a set of fracture curves are derived in terms of the notch stress intensity factors. These curves can be used to predict the mixed mode fracture toughness and the crack initiation angle at the notch tip. An expression is also obtained from this criterion for predicting fracture toughness of U-notched components in pure mode II loading. It is shown that there is a good agreement between the results of UMTS criterion and the experimental data obtained by other authors from three-point bend specimens.     

Determination of T-stress from finite element analysis for mode I and mixed mode I/II loading

The elastic T-stress has been recognised as a measure of constraint around the tip of a crack in contained yielding problems. A review of the literature indicates that most methods for obtaining T are confined to simple geometry and loading configurations. This paper explores direct use of finite element analysis for calculating T. It is shown that for mode I more reliable results with less mesh refinement can be achieved if crack flank nodal displacements are used. Methods are also suggested for calculating T for any mixed mode I/II loading without having to calculate stress intensity factors. There is good agreement between the results from the proposed methods and analytical results. T-stress is determined for a test configuration designed to investigate brittle and ductile fracture in mixed mode loading. It is shown that in shear loading of a cracked specimen T vanishes only when a truly antisymmetric field of deformation is provided. However this rarely happens in practice and the presence of T in shear is often inevitable. It is shown that for some cases the magnitude of T in shear is much more than that for tension. The effect of crack length is also investigated. This revised version was published online in August 2006 with corrections to the Cover Date.     

Fracture of elastomers under static mixed mode: the strain-energy-density factor

This work deals with the fracture of rubbers under a mixed mode loading (I + II) and it is an extension of our previous papers on that subject [Aït Hocine N, Naït Abdelaziz M, Imad A (2002) Int J Fract 117:1–23; Aït Hocine N, Naït Abdelaziz M (2004) In: Sih GC, Kermanidis B, Pantelakis G (eds) 6th international conference for mesomechanics. Patras (Greece), May 31–June 4, pp 381–385]. An experimental and a numerical analysis were carried out using a Styrene Butadiene Rubber (SBR) filled with 20 and 30% of carbon black. Sheets with an initial central crack (CCT specimens) inclined with a given angle compared to the loading direction were used. The J-integral and its critical values J _c (fracture surface energy) were determined by combining experimental data and finite element results. These critical values, determined at the onset of crack growth, were found to be quite constant for each elastomer tested, which suggests that J _c represents a reasonable fracture criterion of such materials. Then, the strain–stress field and the strain-energy-density factor S, earlier introduced by Sih [Sih GC (1974) Int J Fract 10(3):305–321; Sih GC (1991) Mechanics of fracture initiation and propagation. Kluwer Academic Publishers, Dordrecht, 428 pp] were numerically calculated around the crack tip. According to the experimental observations, the plan of crack propagation is perpendicular to the direction of the maximum principal stretch. Moreover, as suggested by Sih in the framework of linear elastic fracture mechanics (LEFM), the minimum values S ^min of the factor S are reached at the points corresponding to the crack propagation direction. These results suggest that the concept of the maximum principal stretch and the one of the strain-energy-density factor can be used as indicators of the crack propagation direction.     

Investigation of mixed mode brittle fracture in rounded-tip V-notched components

A criterion is proposed for brittle fracture analysis in rounded-tip V-notched components. This criterion, called RV-MTS, is developed based on the maximum tangential stress (MTS) criterion proposed earlier for investigating mixed mode brittle fracture in sharp cracks. Using the RV-MTS criterion, a set of fracture curves is presented based on the notch stress intensity factors (NSIFs) for predicting mixed mode and also pure mode II fracture toughness of rounded-tip V-notches. The criterion is also able to predict fracture initiation angles under mixed mode loading. The validity of the criterion is evaluated by several fracture tests performed on the rounded-tip V-notched Brazilian disc (RV-BD) specimens made of PMMA. A good agreement is shown to exist between the theoretical predictions and the experimental results for various notch opening angles and different notch radii.     

Fracture toughness of polycrystalline tungsten under mode I and mixed mode I/II loading

The fracture toughness of swaged polycrystalline tungsten was tested parallel and perpendicular to the swaging direction and under mixed mode I/mode II loading. The fracture mode is dominated by the microstructure and changed from all-transgranular cleavage in mode I to almost all-intergranular fracture in mode II. The mixed mode results can be related to two common failure criteria, the maximum tensile stress criterion (Maximum σ) and the maximum energy release rate criterion (Maximum G), but the large scatter in the data prohibits a clear distinction between the two criteria. Tests at 77 K show that the polycrystal is significantly tougher than the single crystal at this temperature. This is a consequence of the deflection of the crack into the grain boundaries and the imperfect texture (as compared to a single crystal) of the polycrystalline material.     

A new fixture for fracture tests under mixed mode I/II/III loading

In this paper, a new loading device for general mixed mode I/II/III fracture tests is designed and recommended. Finite element analyses are conducted on the proposed apparatus to evaluate the fracture parameters of the tested samples under various mixed mode loading conditions. The numerical results revealed that the designed loading fixture can generate wide varieties of mode mixities from pure tensile mode to pure in‐plane and out‐of‐plane shear modes. The accuracy of the proposed fixture is evaluated by conducting a wide range of fracture tests on compact tension shear (CTS) specimens made of polymethyl methacrylate (PMMA). The experimental results are then compared with the theoretical predictions obtained by the Richard criterion. A good consistency is observed between the experimental results and theoretical predictions.     

Fracture toughness of Ti-15Al-8Nb alloy under mixed mode I/III loading

The effect of mixed mode I/III loading on fracture toughness of Ti-15 at.% Al-8 at.% Nb alloy, which undergoes stress-induced martensitic transformation, was investigated for four different grain sizes. The fracture toughness under mixed mode I/III loading was found to be significantly higher than that under mode I loading in all cases. The results were explained on the basis of the stress and strain fields ahead of a mixed mode crack and its influence on the martensitic transformation zone.     

Crack-tip fields in elastic-plastic material under plane stress mode I loading

New results on the crack-tip fields in an elastic power-law hardening material under plane stress mode I loading are presented. Using a generalized asymptotic expansion of the stress function, higher-order terms are found which have newly-discovered characteristics. A series solution is obtained for the elastic-plastic crack-tip fields. The expansion of stress fields contains both the and terms where t_i is real and t_k is complex; the terms σ⁽ⁱ⁾ _pq(θt_i) and σ^(k) _rsθt_k) are real and complex functions of θ respectively. Comparing the results with that for the plane strain mode I loading shows that: (1) the effect of higher-order solutions on the crack-tip fields is much smaller; and (2) the path-independent integral J also controls the second-order or third-order term in the asymptotic solutions of the crack-tip fields for most of the engineering materials (1 < n < 11) in plane stress, while the J-integral does not control the second and the third-order terms for the plane strain mode I case for n > 3. These theoretical results imply that the crack-tip fields can be well characterized by the J-integral, and can be used as a criterion for fracture initiation under plane stress mode I loading. This is in agreement with existing full-field solutions and experimental data that J at crack growth initiation is essentially independent of in-plane specimen geometry. The comparison confirms the theoretical asymptotic solutions developed in this study. This revised version was published online in August 2006 with corrections to the Cover Date.     

Experimental fracture investigation of CNT/epoxy nanocomposite under mixed mode II/III loading conditions

For the first time, the brittle fracture of epoxy‐based nanocomposite reinforced with MWCNTs (multi‐walled carbon nanotubes) and subjected to mixed mode II/III loading conditions is investigated. This experimental investigation is carried out using a newly developed test configuration. Araldite LY 5052 epoxy, which is a resin frequently used in aerospace industry, is utilized to fabricate pure epoxy and nanocomposite test specimens with two different MWCNTs contents of 0.1 and 0.5 wt%. The obtained experimental results reveal that adding MWCNTs to epoxy resin up to 0.5 wt% improves the fracture toughness under pure mode II and pure mode III loading with an increasing trend. This is while the improvement under mixed mode II/III loading is reduced by adding nanotubes more than 0.1 wt%. To justify the variations of fracture toughness in terms of nanoparticles content, SEM (scanning electron microscopy) photographs of the fracture surfaces of the specimens in the vicinity of the initial crack front are prepared. Additional fracture mechanisms caused by adding carbon nanotubes are discussed in detail based on the provided SEM images.     

Weld root crack propagation under mixed mode I and III cyclic loading

This study examined fatigue propagation behaviour and fatigue life of weld root cracks under mixed mode I and III loading. Fatigue tests were performed on butt-welded joints with a continuous lack-of-penetration (LOP) inclined at angles of 0°, 15°, 30° or 45° to the normal direction of the uniaxial cyclic load. Branch and/or co-planar crack propagation was observed, depending on the initial mode I stress intensity factor (SIF) range. Co-planar crack propagation predominated when the SIF range was large. The fatigue crack propagation mode affected fatigue life; the life of branch crack propagation was longer than that of co-planar crack propagation. Using an initial equivalent SIF range based on a maximum strain energy release rate criterion, the results obtained from the 0°, 15°, 30°, and 45° specimens indicated almost the same fatigue lives, despite the different inclination angles.     

Two-parameter characterization of elastic-plastic crack front fields: Surface cracked plates under tensile loading

In this paper the J-Q two-parameter characterization of elastic-plastic crack front fields is examined for surface cracked plates under uniaxial and biaxial tensile loadings. Extensive three-dimensional elastic-plastic finite element analyses were performed for semi-elliptical surface cracks in a finite thickness plate, under remote uniaxial and biaxial tension loading conditions. Surface cracks with aspect ratios a/c = 0.2, 1.0 and relative depths a/t = 0.2, 0.6 were investigated. The loading levels cover from small-scale to large-scale yielding. In topological planes perpendicular to the crack fronts, the crack stress fields were obtained. In order to facilitate the determination of Q-factors, modified boundary layer analyses were also conducted. The J-Q two-parameter approach was then used in characterizing the elastic-plastic crack front stress fields along these 3D crack fronts. Complete distributions of the J-integral and Q-factors for a wide range of loading conditions were obtained. It is found that the J-Q characterization provides good estimate for the constraint loss for crack front stress fields. It is also shown that for medium load levels, reasonable agreements are achieved between the T-stress based Q-factors and the Q-factors obtained from finite element analysis. These results are suitable for elastic-plastic fracture mechanics analysis of surface cracked plates.     

Analysis of a new specimen for mixed mode fracture tests on brittle materials

Numerical and experimental studies were performed on a new fracture test configuration called the diagonally loaded square plate (DLSP) specimen. The mode I and mode II stress intensity factors were computed for different crack lengths and crack orientation angles using finite element analysis. The numerical results show that the DLSP specimen is able to provide pure mode I, pure mode II and any mixed mode loading conditions in between. Fracture experiments were also conducted on Plexiglas using the DLSP specimen. It is shown that the results obtained from the fracture tests are consistent very well with mixed mode fracture theories.     

The effect of volume fraction of primary α phase on fracture toughness behaviour of Timetal 834 titanium alloy under mode I and mixed mode I/III loading

The effect of volume fraction of primary α phase on mode I and mixed mode I/III fracture toughness of Timetal 834 titanium alloy was investigated. The mode I and mixed mode I/III fracture toughness values for loading angle of 30° were found to initially decrease and subsequently increase with increase in volume fraction of primary α phase. On the other hand, mixed mode I/III fracture toughness for loading angle of 45° was found to monotonically decrease with increasing volume fraction of α phase. The fracture toughness was also found to marginally increase with increasing loading angle for the two lower primary α volume fractions, i.e. 6% and 15% whereas it marginally decreases with increasing loading angle for primary α volume fraction of 30%. The results were explained on the basis of the nature of stress field ahead of the crack tip under mixed mode I/III loading as well as the fracture mechanisms operative in this alloy for different α volume fractions.     

Geometry and size effects on fracture trajectory in a limestone rock under mixed mode loading

The mixed mode I/II fracture initiation angle and the crack growth trajectory of a soft rock (Guiting limestone) were investigated experimentally and theoretically for two different shaped test specimens with various sizes. It was observed that for similar mode mixities in the two specimens, the fracture paths grew in two different trajectories. It is shown that the observed crack path and the fracture initiation angle can be predicted theoretically by using a generalized form of the maximum tangential stress criterion. The main difference in the fracture initiation angles was found to be related to the magnitude and sign of the T-stress.     

Relationship between J-integral and averaged strain-energy density for U-notches in the case of large control volume under Mode I loading

The main purpose of this technical note is to present a relationship between J-integral and averaged strain-energy density () in U-notches under Mode I loading for brittle or quasi-brittle materials. In this work, control volume includes the rectilinear edge of the notch in addition to semi-circular arc of the notch root. A dimensionless function (f) between J and has been presented in this paper. Finite element analysis has been used for verification. It is found that this relationship is identical for tension or bending loading.     

Reference stress based elastic-plastic fracture analysis for circumferential through-wall cracked pipes under combined tension and bending

This paper proposes an engineering method to estimate the J-integral and the crack opening displacement (COD) for circumferential through-wall cracked pipes under combined tension and bending. The proposed method to estimate the COD is validated against three published pipe test data, generated from a monotonically increasing bending load with a constant internal pressure, which shows excellent agreements. Further validation is performed against three-dimensional, elastic-plastic finite element results using actual tensile data of a TP316 stainless steel at the temperature of 288°C. The FE results of the J-integral and the COD, resulting from six cases of proportional and non-proportional combined tension and bending, compare very well with those estimated from the proposed method.Excellent agreements of the proposed method with experimental data and the detailed FE results firstly provide sufficient confidence in the use of the proposed method to the LBB analysis of through-wall cracked pipes under combined tension and bending. More importantly, these validations suggest that the proposed method can be used to any combination of the bending-to-tension ratio, not only for proportional loading but also for non-proportional loading. Finally the proposed method is simple to use, which gives significant merits in practice, and thus is easy to be generalised to more complex situations.     

Quantification of constraint effects in fracture mechanism transition for cracked structures under mixed mode loading

The objective of the study is to evaluate the effects of plastic constraint on transition between tensile-type and shear-type fracture. The T -stress is employed as the quantifying parameter for constraint and is incorporated into the existing theoretical criteria for modelling this transition. It is found that different constraint levels can dramatically alter the transition point. To verify this finding, two sets of mixed mode tests with different constraint levels are carried out. Alongside the theoretical and experimental study, finite element simulation is performed to verify and support these findings. Substantially improved agreement is observed with experimental data if the effect of plastic constraint on transition is included.     

Verification of a non-local stress criterion for mixed mode fracture in wood

An extension of a non-local stress fracture criterion to orthotropic materials based on the damage model of an elastic solid containing growing microcracks was presented in this paper. By taking this approach, a new fracture condition expressed in terms of the mixed mode stress intensity factors for orthotropic materials was proposed and its applicability to predict of a crack initiation and propagation in wood was validated. Predicted values of the stress intensity factors at failure were compared to experimental observations carried out on wood specimens for cracks arbitrarily oriented with respect to the orthotropy axes. Special considerations were applied to the comparison of the non-local stress fracture criterion with some classical fracture criteria for orthotropic materials.