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.     

Investigation of ductile rupture in U‐notched Al 6061‐T6 plates under mixed mode loading

The aim of the present research is to evaluate ductile failure of U‐notched components under mixed mode I/II loading conditions. For this purpose, first, several rectangular plates made of the aluminium alloy Al 6061‐T6 and weakened by central bean‐shaped slit with two U‐shaped ends are tested under mixed mode I/II loading conditions, and the load‐carrying capacity of the specimens are experimentally measured. Then, using the equivalent material concept, Al 6061‐T6, which is a highly ductile material, is equated with a virtual brittle material, and the load‐carrying capacity of the same U‐notched specimens virtually made of the equivalent material is theoretically predicted by using two well‐known stress‐based brittle fracture criteria. Finally, the theoretical failure loads of the virtual specimens are compared with the experimental ones of the real Al 6061‐T6 specimens. It is revealed that the experimental results could very well be predicted by means of both brittle fracture criteria without conducting time‐consuming elastic–plastic analyses.     

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 novel fixture for mixed mode I/II/III fracture testing of brittle materials

A novel test‐loading device was suggested in order to study the fracture behavior of brittle materials under mixed mode I/II/III loading conditions. A version of the compact tension shear specimen was used as the test configuration. Using a three‐dimensional finite element analysis, the influence of mode mixity on the stress intensity factors, the T‐stress, and 3‐D plastic zone around the crack tip was investigated. In addition, an experimental study was performed on an epoxy polymer using the proposed setup. Finally, the fracture toughness of pure epoxy was measured under several loading conditions. The numerical and experimental results manifested that the proposed setup is able to determine a full range of mixed mode I/II/III fracture properties. At the end, the fracture envelope obtained using the practical study was compared with various three‐dimensional fracture criteria. A negligible discrepancy was concluded between the practical data and the theoretical data estimated by the maximum mean principle stress criterion.     

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.     

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.     

The role of T-stress in brittle fracture for linear elastic materials under mixed-mode loading

The purpose of this paper is to revisit the maximum tensile stress (MTS) criterion to predict brittle fracture for mixed mode conditions. Earlier experimental results for brittle fracture of polymethylmethacrylate (PMMA) using angled cracked plates are also re-examined. The role of the T -stress in brittle fracture for linear elastic materials is emphasized. The generalized MTS criterion is described in terms of mode I and II stress intensity factors, K _I and K _II and the T- stress (the stress parallel to the crack), and a fracture process zone, r _c . The generalized MTS criterion is then compared with the earlier experimental results for PMMA subjected to mixed mode conditions. It is shown that brittle fracture can be controlled by a combination of singular stresses (characterized by K ) or non-singular stress ( T -stress). The T -stress is also shown to have an influence on brittle fracture when the singular stress field is a result of mode II loading.     

Can pure mode III fatigue loading contribute to crack propagation in metallic materials?

The possibility of pure mode III crack growth is analysed on the background of theoretical and experimental results obtained in the last 20 years. Unlike for modes I and II, there is no plausible micromechanistic model explaining a pure mode III crack growth in ductile metals. In order to realize 'plain' mode III fracture surface, we propose the propagation of a series of pure mode II cracks along the crack front. Fractographical observations on crack initiation and propagation in a low alloy steel under cyclic torsion support such a model. The authors have not seen any clear indication of a pure mode III crack growth micromechanism in metals until now.     

Temperature effects on mixed mode I/II delamination under quasi-static and fatigue loading of a carbon/epoxy composite

This paper addresses the effect of temperature on the mixed-mode interlaminar fracture toughness and fatigue delamination growth rate of a carbon-fibre/epoxy material, namely IM7/8552. Quasi-static and fatigue characterisation tests were carried out at −50 °C, 20 °C, 50 °C and 80 °C, using asymmetric cut-ply coupons. The experimental results show that temperature may have an accelerating or delaying effect on delamination growth, depending on the loading regime, i.e. either quasi-static or fatigue. Fractographic examinations were also carried out in order to assist the interpretation of the experimental data. A semi-empirical equation is introduced to describe the experimentally observed fatigue delamination growth rates at elevated temperatures.     

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.     

Fracture and fatigue study of unidirectional glass/epoxy laminate under different mode of loading

Interlaminar fracture is the dominant failure mechanism in most advanced composite materials. The delaminating behaviour of materials is quantified in terms of the strain energy release rate G. In this paper, the experimental measurements of the fatigue delaminating growth for some combinations of energy release rate mode ratio have been carried out on unidirectional glass/epoxy laminates. On this base the constants in the Paris equation have been determined for each G_II/G_T considered modal ratio. The fatigue threshold strain energy release rate Δ G_Tth , below which delaminating doesn't occur, were measured. Three type specimens were tested, namely: double cantilever beam (DCB), end‐loaded split (ELS) and mixed‐mode bending (MMB) under mode I, mode II and mixed‐mode (I + II) loading, respectively. Scanning electron microscopy techniques were used to identify the fatigue delamination growth mechanisms and to define the differences between the various modes of fracture.     

Analytical solutions for crack-tip sectors in perfectly plastic Mises materials under mixed in-plane and out-of-plane shear loading conditions

In this paper, analytical solutions for asymptotic crack-tip plastic sectors in perfectly plastic Mises materials are derived under mixed in-plane and out-of-plane shear loading conditions. Plastic strains in crack-tip plastic sectors are considered to be singular and non-singular. Sectors with singular plastic strains have the solution of centered fan type, and sectors with non-singular plastic strains have the solution of either centered fan or constant stress type. The requirement of stress continuity along the border between a constant stress and a centered fan sectors is then discussed. Discontinuities of the normal and out-of-plane shear stresses in the radial direction between two constant stress sectors are assumed in assembling the crack-tip fields under mixed mode II/III and I/III conditions. Crack-tip fields under mixed mode II/III and I/III conditions with small contributions of mode III are then presented to show the existence of asymptotic crack-tip fields for perfectly plastic materials under mixed in-plane and out-of-plane shear loading conditions. The trends of the angular variations of the mode III stresses under the mixed mode II/III and I/III conditions are generally in agreement with those of the available asymptotic and finite element analyses for low strain hardening materials.     

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.     

Effect of temperature on the mode I and mixed mode I/III fracture toughness of SA333 steel

The effect of temperature on tensile properties, mode I and mixed mode I/III fracture toughness of SA333 Grade 6 steel was investigated. The variation of ultimate tensile strength and strain hardening exponent with temperature as well as the appearance of serrations in the stress-strain plots indicated that dynamic strain aging regime in this steel is in the temperature range 175-300 °C at a nominal strain rate of 3 × 10⁻³ s⁻¹. Both mode I and mixed mode I/III fracture toughness values were found to exhibit a significant reduction in the DSA regime. The mixed mode I/III fracture toughness was found to be significantly lower than the mode I fracture toughness at all temperatures. However, the difference between the two toughness values was much higher prior to the onset of DSA. The results are explained on the basis of the nature of deformation fields under mode I and mixed mode I/III loading as well as the fracture mechanism prevalent in these steels at different temperatures.     

Numerical and experimental investigation of mixed‐mode fracture parameters on silicon nitride using the Brazilian disc test

Engineering applications of ceramics can often involve mixed‐mode conditions involving both tensile and shear loading. Mixed‐mode fracture toughness parameters are evaluated for applicability to ceramics using the Brazilian disc test on silicon nitride. Semi‐elliptical centrally located surface flaws are induced on the disc specimens using Vickers indentation and compression loaded to fracture with varying levels of mode mixity. The disc specimens are modelled via 3D finite element analysis and all three modes of stress intensity factors computed along the crack front, at failure load. We present a numerical and experimental investigation of four widely used mixed‐mode fracture criteria and conclude that the critical strain energy release rate criterion is simple to implement and effective for silicon nitride under mixed‐mode conditions.     

Face/core interface fracture characterization of mixed mode bending sandwich specimens

Debonding of the core from the face sheets is a critical failure mode in sandwich structures. This paper presents an experimental study on face/core debond fracture of foam core sandwich specimens under a wide range of mixed mode loading conditions. Sandwich beams with E‐glass fibre face sheets and PVC H45, H100 and H250 foam core materials were evaluated. A methodology to perform precracking on fracture specimens in order to achieve a sharp and representative crack front is outlined. The mixed mode loading was controlled in the mixed mode bending (MMB) test rig by changing the loading application point (lever arm distance). Finite element analysis was performed to determine the mode‐mixity at the crack tip. The results showed that the face/core interface fracture toughness increased with increased mode II loading. Post failure analysis of the fractured specimens revealed that the crack path depends on the mode‐mixity at the crack tip, face sheet properties and core density.     

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.     

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.     

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.