Mixed-mode fracture in biaxial stress state: Application of the diametral-compression (Brazilian disk) test

Mixed-mode fracture of soda-lime glass was studied using a diametral-compression test that features disk specimens with symmetric through-cracks. The test enables one to study fracture under pure mode I loading, pure mode II loading, or any combination of mode I and mode II loading by a simple alignment of the crack relative to the diameter of compression loading. The disk specimens were precracked with the aid of both chevron notches and water-assisted subcritical crack growth. The directions of noncoplanar crack extensions and the relative magnitudes of mode I and mode II stress-intensity factors for mixed-mode fracture under inert conditions were compared to the predictions of three different mixed-mode fracture theories. None of the theories was completely adequate to explain the experimental observations, but a maximum hoop stress criterion modified to include second order, nonsingular term in the series solution for the crack-tip region stress gave reasonable agreement with the experimental results.     

Connecting the essential work of fracture, stress intensity factor, Hill’s criterion in mixed mode I/II loading

Ductile sheet structures are frequently subjected to mixed mode loading, resulting that the structure is under the influence of a mixed mode stress field. Instances of interest are when stable crack growth occurs and when the crack-tip is propagating in this complex mixed-mode condition, prior to final fracture. Purposely designed apparatus was built to test thin-sheets of steel (Grade: DX51D) under mixed-mode I/II. These tests, under plane stress conditions, also investigated the effect of thickness on the specific essential work of fracture or the fracture toughness of the material under quasi-static cracking conditions. The fracture toughness is evaluated under incremental mixed-mode loading conditions. The direction of the propagating crack path and fracture type were observed and discussed as the loading mixity was varied. Whilst the specific essential work of fracture or fracture toughness was obtained using the energy approach, the theoretical analysis of the fracture type and direction of crack path were based on the crack tip stresses and fracture criterions of maximum hoop stress and maximum shear stress along with the utilisation of Hill’s theory. For mixed-mode I/II loading, the variation in the fracture toughness contributions ratios are evaluated and used predicatively using the established energy criterion approach to the crack tip stress intensity approach. The comparison between the theoretical directions of the crack path, failure mode propagation are in good agreement with those obtained from experimental testing indicating the definite link between both approaches.     

On the calculation of derivatives of stress intensity factors for multiple cracks

In this paper, the work of Lin and Abel [Lin SC, Abel JF. Variational approach for a new direct-integration form of the virtual crack extension method. Int J Fract 1988;38:217-35] is further extended to the general case of multiple crack systems under mixed-mode loading. Analytical expressions are presented for stress intensity factors and their derivatives for a multiply cracked body using the mode decomposition technique. The salient feature of this method is that the stress intensity factors and their derivatives for the multiple crack system are computed in a single analysis. It is shown through two-dimensional numerical examples that the proposed method gives very accurate results for the stress intensity factors and their derivatives. It is also shown that the variation of mode I and II displacements at one crack-tip influence the mode I and II stress intensity factors at any other crack. The computed errors were about 0.4-3% for stress intensity factors, and 2-4% for their first order derivatives for the mesh density used in the examples.     

Thermomechanical coupling effects on fractured solids

An analytical model is presented to predict the temperature field induced in a fractured solid by mechanical loadings. The heat conduction equation used to compute the temperature field consists of three separate terms that account for the coupling effects. These are the thermoelastic, thermoplastic and thermofracture coupling terms. Finite element formulations were used for the numerical solutions of a case study. This case study involved experimental assessments of temperature rises near the tip of a stationary crack when subjected to an impact load that attempted to open the crack surfaces. Good correlations of analytical and experimental results were obtained. The measurable temperature rises in a fractured solid suggested that the coupling effect may be significant enough to influence the fracture characteristics of a solid; in particular, if the bulk temperature of the solid is close to the transition temperature from the brittle to ductile fracture mode or vice versa.     

Mode II Brittle Fracture Assessment Using ASFPB Specimen

The four-point bend specimen subjected to anti-symmetric loading (ASFPB) is frequently used for determining pure mode II fracture resistance of rock materials. It is shown in this paper that, when the applied loads are close to the crack plane, the ASFPB specimen does not provide pure mode II condition, since the effect of mode I also appears in crack tip deformation. A set of fracture test were also conducted on a type of marble using ASFPB configuration. The test results showed that fracture resistance is strongly dependent on the loading distance from the crack plane. The effective fracture toughness increases when the distance between the loading points and the crack plane decreases. It is shown that the enhanced fracture resistance of marble samples could be mainly because of very large negative T-stresses that exist for the mentioned loading situations.     

Strain and stress fields near the blunted tip of a crack under mixed mode loading and the implications for fracture

The strain distribution in the vacinity of a blunted crack-tip is analysed by slip line theory under the conditions of plane-strain, small-scale yielding, and mixed-mode loading of Modes I and II. A generalized crack-tip opening displacement is introduced by which the strain and stress fields near the blunted crack-tip are determined uniquely over a wide range of Mode I and II combinations. Also, coupled experimental and finite-element analyses under the condition of large-scale yielding reveal that the initiation of stable crack growth occurs when the generalized crack-tip opening displacement attains a critical value which is constant for the material tested. The finite-element analysis is based on the finite deformation theory of elastic-plastic materials. The generalized crack-tip opening displacement criterion is found to be superior to the J-integral and the usual COD for the characterization of the initiation of stable crack growth. The plastic work in a small circular region at the crack-tip is found to be equivalent to the generalized crack-tip opening displacement, as a fracture criterion.     

Mikrofraktographie an CFK mit thermoplastischer Matrix (APC-2)

Microfractography of CFRP with thermoplastic matrix(APC-2) The objective of this investigation was to find out microfractographic features for APC-2 material due to specific loading modes. Interlaminar fractures were produced using static mode. I, II and mixed mode loading. Simultaneously, the fracture thoughness were measured. Furthermore, we determined the influence crack growth velocity and the temperature on the fracture morphology. Due to the three loading modes we got fraction surfaces with local changing ductil and brittel fracture morphologies but respectively specific for each mode. The ductil fracture morphology corresponds to lower and the brittle one to higher crack growth velocity. The area with the ductil fracture morphology increases with decreasing crack growth velocity and increasing temperature. At the same time the fracture thoughness of the material increases. This is an under-standable correlation. At loading modes with a tensil stress component (mode I and mixed mode) we found arest lines (lines in which the local crack growth velocity changes) in the fracture surface regions with a brittle fracture morphology. With the help of these arest lines the crack growth direction can be determined. At mode II loadings only the direction of the shear stress can be detected due to the microfractographic deformation direction. Interlaminar fatigue fractures (in notched bending specimens) show specific fracture morphologies which are influenced from the spherolithic microstructure of the semicrystalline matrix. A breakup of the PEEK -matrix in fibrils starting at the fibres is visible. This can be probably traced back to delamination of the amorphous fibrils and a breakup of the crystalline lamellas. On principle CFRP with a thermoplastic matrix has a completely different fracture morphology as a composite with a thermoset epoxy matrix. This is clear if one considers that the fracture strain of PEEK is one order higher than that of epoxy.     

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.     

Mixed-mode fracture of ductile thin-sheet materials under combined in-plane and out-of-plane loading

Cracks in thin structures often are subjected to combined in-plane and out-of-plane loading conditions leading to complex mixed mode conditions in the crack tip region. When applied to ductile materials, large out-of-plane displacements make both experimentation and modeling difficult. In this work, the mixed-mode behavior of thin, ductile materials containing cracks undergoing combined in-plane tension (mode I) and out-of-plane shear (mode III) deformation is investigated experimentally. Mixed-mode fracture experiments are performed and full, three-dimensional (3D) surface deformations of thin-sheet specimens from aluminum alloy and steel are acquired using 3D digital image correlation. General characteristics of the fracture process are described and quantitative results are presented, including (a) the fracture surface, (b) crack path, (c) load-displacement response, (d) 3D full-field surface displacement and strain fields prior to crack growth, (e) radial and angular distributions of the crack-tip strain fields prior to crack growth and (f) singularity analysis of the crack-tip strains prior to crack growth. Results indicate that the introduction of a mode III component to the loading process (a) alters the crack tip fields relative to those measured during nominally mode I loading and (b) significantly increases the initial and stable critical crack-opening-displacement. The data on strain fields in both AL6061-T6 aluminum and GM6208 steel consistently show that for a given strain component, the normalized angular and radial strains at all load levels can be reasonably represented by a single functional form over the range of loading considered, confirming that the strain fields in highly ductile, thin-sheet material undergoing combined in-plane tension and out-of-plane shear loading can be expressed in terms of separable angular and radial functions. For both materials, the displacement and strain fields are (a) similar for both mixed-mode loading angles Φ = 30° and Φ = 60° and (b) different from the fields measured for Mode I loading angle Φ = 0°. Relative to the radial distribution, results indicate that the in-plane strain components do not uniformly exhibit the singularity trends implicit in the HRR theory.     

Crack resistance and micromechanisms of fracture of thermomechanically treated high-strength steel

We study the influence of thermomechanical treatment with deformation by the method of hydrostatic extrusion on the parameters of crack resistance of 45KhN2MFSh high-strength steel and plot the dependences of the critical stress intensity factorK _Ic and critical crack opening displacements δ_c on temperature. It is shown that these curves have the threshold character. The results of microfractographic analysis demonstrate that changes in crack resistance observed as temperature decreases are accompanied by changes in the micromechanisms of fracture in the regions of the onset of crack propagation, which may take place under the condition of changes in the second-order stress-strain state. We show that the temperature curves of the parameters of crack resistance can be efficiently used in determining the temperature of brittle-ductile transition. In the considered case, this temperature does not depend on the size of the specimen and the loading mode and characterizes the structural state of the cracked material. As compared to conventional modes of thermal treatment, thermomechanical treatment guarantees much higher values of crack resistance, especially at low temperatures, and decreases the threshold of cold brittleness for 45KhN2MFSh steel by 20°C. The indicated increase in crack resistance is explained by the hereditary influence of the deformational substructure on the structural and morphological parameters of martensite. Khar'kov State Technical University of Automobiles and Roads, Khar'kov. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 33, No. 3, pp. 82–86, May–June, 1997.     

Hybrid finite element analysis of transient thermoelastic fracture problems subjected to general heat transfer conditions

This paper presents the singular characteristics of heat flux in the vicinity of the crack-tip for two dimensional transient thermoelastic fracture problems subjected to general heat transfer conditions at crack surfaces. Based on a restricted variational principle, a rigorous hybrid finite element procedure is then developed to perfectly describe the singularities of heat flux and thermal stress induced at the crack-tip. For verification purposes, the examples of transient thermoelastic problems with insulated crack surfaces are first analyzed. Excellent agreements between the computed results and referenced solutions can be drawn. To evaluate the influence of heat convection and radiation on the computation of temperature distributions and thermal stress intensity factors, several numerical examples are also presented.     

Effect of thermomechanical loads on the propagation of crack near the interface brittle/ductile

The purpose of this paper is to understand the combined effect of thermal and mechanical loading on the initiation and behaviour of sub-interface crack in the ceramic. In this study a 2D finite element model has been used to simulated mixed mode crack propagation near the bimaterial interface. The assembly ceramometalic is subjected simultaneously to thermomechanical stress field. The extent of a plastic zone deformation in the vicinity of the crack-tip has a significant influence on the rate of its propagation. The crack growth at the joint specimen under four-point bending (4PB) loading and the influence of residual stresses was also evaluated by the maximum tensile stress criterion. The J-integral at the crack tip is generally expressed by the thermomechanical local stresses. The results obtained show the effect of the temperature gradient ΔT, the size of the crack and the applied stresses on the J-integral.     

A critical shear displacement criterion for ductile–brittle transition under mixed mode I and II loading

Abstract

Micromechanisms producing ductile and brittle damage operate in parallel at a crack tip. The dominant mode of failure depends upon which of the two (ductile or brittle) damage parameters first reaches its critical value. This has been shown by a study of ductile–brittle transition behaviour in HY100 steel under mixed mode I and II loading. The transition from ductile to brittle behaviour in HY100 steel was found to be affected by mixed mode I and II ratio (ratio of imposed tensile and shear loading) in a manner such that with increasing shear the transition temperature decreased. In the present paper, a criterion is proposed based on the shear strain ahead of a notch tip, to predict the fracture behaviour at any given temperature and mixed mode ratio.     

Experimental characterization of dynamic crack growth behavior in CFRP adhesive interface

The dynamic crack growth behavior of adhesively bonded joints under mode I and mixed mode (I + II) loading were investigated. The split Hopkinson pressure bar (SHPB) apparatus and the digital image correlation (DIC) technique were employed to determine the mode I fracture toughness of the adhesively bonded joints during crack propagation under impact loading. The dynamic crack growth behavior for carbon fiber reinforced plastics (CFRP) adhesively bonded joints under mode I loading was studied using this method. In order to verify the proposed method, the dynamic crack growth behavior of titanium alloy adhesively bonded joints was also studied. Moreover, the crack growth behavior of CFRP adhesively bonded joints under mixed mode loading was studied using the SHPB technique. For the considered CFRP adhesively bonded joints, the fracture toughness decreased under both mode I and mixed mode loading as the loading rate increased. Microscope observation showed that a shift in the crack location occurred in the high loading tests.     

Mixed mode I/II fracture of 2024-T3 friction stir welds

For the first time, a series of mixed mode I/II fracture experiments have been performed on both base material and three families of friction stir welds (FSWs) in 6.4 mm thick, 2024-T351 aluminum plate; the FSW joints are designated hot, medium and cold due to the level of nominal weld energy input per unit weld length (specific weld energy) during the joining process.Results from the fracture tests indicate that the measured critical crack opening displacement (COD) at a fixed distance behind the crack tip properly correlates both load-crack extension response and microstructural fracture surface features for both the base metal and all FSWs, providing measure of a quantitative fracture toughness. The COD values also indicate that transition from mode I to mode II dominant crack growth occurs at lower loading angles for FSW joints having higher specific weld energy input, with a truly mixed mode I/II COD measured during crack growth in the medium FSW joint. Using results from recent detailed FSW metallographic studies, specific features in the fracture process are correlated to the FSW microstructure. Finally, the observed ductile crack growth path in all three welds tends to exit the under-matched FSW weld region as the far-field applied shear loading is increased, with the medium FSW being the only case where the flaw remained within the FSW region for all combinations of shear and tensile loading.     

A revised virtual crack closure technique for physically consistent fracture mode partitioning

The virtual crack closure technique (VCCT) is a well-established method for computing the energy release rate when analysing fracture problems via the finite element method. For mixed-mode fracture problems, the VCCT is also commonly used to partition the fracture modes, i.e. to determine the energy release rate contributions related to the three classical fracture modes. A perhaps little known fact, however, is that in some circumstances the standard VCCT predicts physically inconsistent, negative values for the modal contributions to the energy release rate. Focusing on I/II mixed-mode problems, this paper presents a revised VCCT which furnishes a physically consistent partitioning of fracture modes by associating the mode I and II contributions to the amounts of work done in a suitably defined two-step process of closure of the virtually extended crack. Deeper investigation pinpoints the origins of the physically inconsistent predictions of the standard VCCT in the lack of energetic orthogonality between the crack-tip force components used to compute the modal contributions. Further insight into the problem is offered by a geometric construction, which introduces the ‘ellipse of crack-tip flexibility’. In closing, the phenomena of contact, interpenetration, and friction between the crack surfaces are briefly touched upon.     

An improved semi-circular bend specimen for investigating mixed mode brittle fracture

An edge cracked semi-circular specimen subjected to asymmetric three-point bend loading was suggested for investigating mixed mode fracture in brittle materials. Using finite element analysis, the crack parameters were obtained for various crack lengths and different locations of loading points. It was shown that by selecting appropriate positions for the loading points, full mode mixities from pure mode I to pure mode II could be achieved. Then, a series of fracture tests were conducted on PMMA using the proposed specimen. Very good agreement was found between the experimental results and those predicted from the generalized maximum tangential stress criterion.     

Interlaminar fracture characterization for plain weave fabric composites

For the analysis of laminated composite plates under transverse loading and drilling of composites, all the elastic, strength and fracture properties of the composite plates are essential. Interlaminar critical strain energy release rate properties in mode I, mode II, mixed mode I/II and mode III have been evaluated for two types of plain weave fabric E-glass/epoxy laminates. The double cantilever beam test and the end notch flexure test have been used for mode I and mode II loading. The mixed mode bending test and split cantilever beam test have been used for mixed mode I/II and mode III loading. It is observed that the plain weave fabric composite with lesser strand width has higher interlaminar fracture properties compared to the plain weave fabric composite with more strand width. Further, crack length versus crack growth resistance plots have been presented for mode III loading. In general, it is observed that total fracture resistance is significantly higher than the critical strain energy release rate.     

Analysis of interfacial cracks in a TBC/superalloy system under thermal loading

Thermal barrier coatings (TBCs) provide thermal insulation to high temperature superalloys. Residual stresses develop in TBCs during cool down from processing temperatures and subsequent thermal cyclic loading due to the thermal expansion mismatch between the different layers (substrate, bond coat, and TBC). These residual stresses can initiate microcracks at the bond coat/TBC interface and can lead to debonding at the bond coat/TBC interface. The highest residual stresses occur at the interfaces. The effect of voids or crack like flaws at the interface can be responsible for initiating debonding and accelerate the oxidation process. The effect of interfacial microcracks has been investigated using the fracture mechanics approach. In particular, J-integral and the energy release rate G, for both mode I and mode II using the virtual crack extension method were evaluated. Two types of specimens were studied. The specimens were cooled down from processing temperature of 1000°C to 0°C. The variation of the properties as a function of temperature were used for the analysis. It was found that the use of temperature dependent properties in contrast to constant properties provide significantly different values of J-integral and G. For the stepped-disc specimen with an edge crack, crack growth is only due to mode II, while for the cylinder specimen with an internal crack, crack growth is due to mixed-mode loading. An important implication of this result is that edge delaminations in a disk specimen may only grow due to mode II conditions under pure thermal loading. Shear fracture characteristics of interfacial crack thus become important in the failure of the TBC.     

Transformation zones, crack shielding, and crack-growth resistance of Ce-TZP/alumina composite in mode II and combined mode II and mode I loading

Crack-tip transformation zones, crack shielding and crack-growth-resistance (R-curve) behaviors of a transformation-toughened ceria-partially stabilized zirconia–alumina (Ce-TZP/alumina) composite were studied in mode II and combined mode I and mode II loading using compact-tension-shear (CTS) specimens. The mode II and mode I stress intensities for both the initial straight cracks and the subsequent kinked cracks were assessed by the method of caustics using geometrically equivalent specimens of polymethyl methacrylate (PMMA). The angle of formation of the transformation zones as well as of extension of the cracks increased systematically with increasing ratio of the mode II and the mode I stress intensities and approached a value of θ^*=−72° in pure mode II loading. This angle was close to the angle for maximum hoop tension in the stress field of a mode II crack (θ^*=−70.5°). A crack-initiation toughness envelope was constructed on a K_I–K_II diagram using the critical loads for incremental crack extension. The crack-initiation toughness in pure mode II loading was less than the corresponding toughness in mode I loading. This result was consistent with calculations that indicated no shielding from the asymmetric and elongated zones developed in mode II loading. The fracture toughness measured for the kinked cracks at long kink lengths approached the maximum fracture toughness measured for a mode I crack.