Damage zone around crack tip and fracture toughness of rubber-modified epoxy resin under mixed-mode conditions

Damage zones that form around crack tips before the onset of fracture provide significant data for evaluating the fracture behavior of polymeric materials. The size of the damage zone correlates closely with the fracture toughness of the resin. In this study, we investigate the relationship between the fracture toughness and damage zone size around crack tips of a rubber-modified epoxy resin under mixed-mode conditions. The fracture toughness, G_C, based on the energy release rate, is measured using an end-notched circle type (ENC) specimen. The deformation of rubber particles in the damage zones is also observed using an optical microscope. The results show that the fracture toughness, G_C, of the rubber-modified epoxy resin is closely related to the area of the damage zone. In the specimen with a loading angle of 30°, the rubber particles were deformed ellipsoidally due to the difference between the first and second principal stresses.     

Effect of mixed mode I/II on fracture behaviour of laminated metal matrix composites

Abstract

The effects of mixed mode loading (I/II) on the fracture toughness and fracture behaviour of both 6090/SiC/20_p-6013 diffusion bonded laminates and 2080/SiC/20_p-2080 adhesive bonded laminates tested in the crack arrester orientation were investigated. The effects of layer thickness and volume fraction ratio on the fracture behaviour under the mixed mode were also studied. The fracture behaviour under mode I/II of available similar discontinuously reinforced aluminium (DRA) materials was additionally compared to that of the laminates. The fracture behaviour of laminates under mode I/II was dependent on the volume fraction ratio and generally different from that of the monolithic and DRA. The increase in the fracture toughness of DRA by lamination with ductile layers under mode I changes somewhat under increasing load mixity, for 75/25 and 50/50 diffusion bonded laminate and 60/40 adhesive bonded laminate ABL. This results from extensive interfacial separation and delamination between the layers.     

Interlaminar and intralaminar fracture characterization of composites under mode I loading

The interlaminar and intralaminar fracture of laminated composites under mode I loading was studied using the double cantilever beam test. The effect of bridging on the measured fracture energy was assessed by cutting fibres during crack propagation. The fracture energy was evaluated considering a previously developed data reduction scheme based on the beam theory and crack equivalent concept. The model only requires the applied load–displacement data and provides a complete R-curve allowing the definition of the critical energy from the plateau value. A cohesive damage model was used to validate the procedure. It was verified experimentally that bridging phenomenon is pronounced, being more important in intralaminar tests. However, a detailed observation of the intralaminar R-curves showed that the intrinsic toughness, without fibre bridging effects, is similar to the interlaminar one.     

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.     

Creep Crack Growth in Polyethylene Under Combined Mode I and Mode II Loading

Creep crack growth characteristics under various combined mode I and mode II loadings were studied using the compact tension shear (CTS) specimens of polyethylene. Creep crack growth rates da/dtunder combined mode I and mode II loading can be correlated with a single effective stress intensity factor K _Ieffderived from the combined — mode fracture toughness envelope. The steady state or constant crack growth rates which occupy the significant part of creep failure life increase with the increasing initial effective stress intensity factor.     

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.     

R-curve behaviour of PZT ceramics near the morphotropic phase boundary

The mechanical failure of PZT ceramics was characterized by measuring R-curves for compositions near and at the morphotropic phase boundary (MPB) where tetragonal and rhombohedral phases coexist in equal quantities. The R-curve behaviours (an increasing fracture toughness with crack extension) were identified by indentation-fracture testing and they were analysed to determine the key parameters. The fracture toughness of the PZT ceramics consisted of three different terms, representing particular microstructural processes in front of advancing cracks, that is, intrinsic cleavage, 90° domain switching and microcracking. Their relative contributions to an overall crack-extension resistance varied with the length of the advancing crack and, more importantly, with the compositions of the PZT. In the compositional range where the tetragonal phase was dominant, the R-curves were determined by domain switching and microcracking. However, the compositional dependency of the fracture toughness was due to the microcracking mechanism. On the other hand, in regions rich in rhombohedral phases, the R-curves were essentially determined by domain switching in the crack-tip area. The R-curves characterized by the domain-switching mechanism were insensitive to the compositional variation near the MPB. Our results also demonstrated that R-curve analysis could be used to probe further into the microstructural responses of materials in front of advancing cracks and to quantify them particularly in systems like PZT where several different toughening processes compete with each other.     

Comparison of shear and tensile fracture in high strength aluminum alloys

A comparison was made between tensile (mode I) and shear (mode II) fracture characteristics in high strength aluminium alloys (7075-T6 and 6061-T651) using a relatively new mode II fracture specimen to evaluate the critical stress intensity factor. The enlarged plastic zone during mode II fracture required that an increased specimen thickness be used for determining K _Hc under a purely plane strain condition. Plane stress conditions prevailed in the mode II fracture of 7075-T6 with a specimen thickness less than 10 mm, while plane strain controlled mode II fracture at a thickness of 10 mm or greater. Fractographic analysis revealed a distinctive difference in the micromechanisms responsible for crack extension. Small dimples were observed only on the mode II fracture surfaces, resulting from a microvoid nucleation fracture mechanism. The mode I fracture surfaces showed a mixed distribution of dimple sizes resulting from a void growth fracture mechanism. Comparing the critical stress intensity factors, the shear mode of failure exhibited a substantially higher value than the tensile mode, resulting from the effect of the sign and magnitude of the hydrostatic stress state on the microvoid nucleation event. Zero hydrostatic tension in the mode II loading configuration helps delay microvoid nucleation, increasing the apparent toughness. The high hydrostatic tension resulting from a mode I loading configuration enhances microvoid nucleation which promotes crack propagation at relatively lower stress intensity factors.     

Study of elastic-plastic fracture toughness determination

The elastic-plastic fracture toughness viaJ-integral and crack tip opening displacement (CTOD) has been obtained in two structural steels using several fitting equations representing the resistance curve of the material. The toughness is determined as the values corresponding to the critical stretched zone width (SZW) on theR-curves and with respect to 0.2 mm crack growth. The SZW measurements were performed by scanning electron microscopy. The various toughness values have been compared and the importance of using appropriateR-curves based on physical considerations has been pointed out. TheJ-CTOD relationship during the blunting process has been experimentally investigated from load-displacement records of the fracture test.     

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.     

Weight function approach for determining crack extension resistance based on the cohesive stress distribution in concrete

The use of universal form of weight functions for determining the K_R-curves associated with the cohesive stress distribution for complete fracture process of three-point bending notched concrete beam is reported in the paper. Closed form expressions for the cohesion toughness with linear and bilinear distribution of cohesive stress in the fictitious fracture zone during monotonic loading of structures are obtained. Comparison with existing analytical method shows that the weight function method yields results without any appreciable error with improved computational efficiency. The stability analysis and the size-effect study using K_R-curves of crack propagation are also described.     

A FRACTURE CRITERION FOR CRACKS UNDER MIXED-MODE LOADING

Abstract A fracture criterion is proposed, based on maximum energy release rates at the tips of short kinks when the main cracks are subjected to mixed mode loading. The criterion differs from existing energy based criteria in that the fracture toughness, g_c, is not independent of the stress mode prevailing in the region of the tip of the kink but is a function of the ratio of the mode II to mode I stress intensity factors at the tip of the kink, i.e., g_c is determined directionally by an elliptical region with major and minor axes equal to the fracture resistances of the material, K_Ir and K_IIr, for pure mode I and pure mode II, respectively. Points inside the elliptical region are considered safe. When K_IIr is equal to K_Ir the ellipse degenerates into a circle and the fracture criterion reverts to the existing familiar maximum energy release rate criterion based on a single value of the fracture toughness, irrespective of the active mode prevailing in the region at the tip of the kink. In this case, under pure shear (mode II) applied load, K_II, the angle of inclination of the fracture crack extension to the main crack, α, is in the region of ?76°, in general agreement with previous well established results. However, when the ratio r (=K_IIrK_Ir) is less than r′ (=0.82, approximately) a different pattern emerges and, in particular, under pure mode II load, the crack advance is co-planar with the main crack, i.e., in mode II. A lower transition value r″ (=0.582, approximately) was also detected under pure mode I applied load. Thus for values of r≥r″, the crack extension is in pure mode I and is co-planar with the main crack but when r < r″, the crack branches out at an angle (which can be positive or negative) in mixed modes I/II crack extension. Some implications of these results are discussed.     

Fracture behaviour of unmodified and rubber-modified epoxies under hydrostatic pressure

The fracture toughness and uniaxial tensile yield strengths of unmodified and CTBN-rubber-modified epoxies were measured under hydrostatic pressure. The purpose of these experiments was to learn how suppressing cavitation in rubber particles affects the deformation mechanisms and the fracture toughness of rubber-modified epoxy. It was found that the cavitation of CTBN-rubber could be suppressed at a relatively low pressure (between 30 and 38 M Pa). With cavitation suppressed, the rubber particles are unable to induce massive shearyielding in the epoxy matrix, and the fracture toughness of the rubber-modified epoxy is no higher than that of the unmodified epoxy in the pressure range studied. Unmodified epoxy shows a brittle-to-ductile transition in fracture toughness test. The reason for this transition is the postponement of the cracking process by applied pressure.Work performed while on a sabbatical leave at the University of Michigan.     

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.     

Interlaminar fracture (model II) of commingled yarn-based GF/PP composites

A 5050 wt % mixture of commingled glass/polypropylene fibre system was selected to study the correlations between the morphological details, mode II interlaminar fracture toughness and corresponding failure mechanisms. Mode II interlaminar fracture tests were performed by using the end-notched flexure test procedure. Compared to conventional composite laminates, mode II interlaminar crack extension in these commingled yarn-based composites was very stable, and extensive fibre nesting occurred along the main crack plane. Crack jumping and non-broken matrix links were observed.R-curve behaviour for these materials was identified and the toughness for initiation was much lower than that for propagation. Compared to mode I interlaminar fracture toughness, similar trends in effects of cooling rates and isothermal crystallizations on mode II interlaminar fracture toughness were observed. However, the effects were not as significant as those found for mode I interlaminar fracture toughness.Alexander von Humboldt Fellow.     

FATIGUE CRACK GROWTH BEHAVIOUR AND FRACTURE RESISTANCE IN CERAMICS

Fatigue crack growth and the fracture resistance curve (R-curve) were investigated in a polycrystalline alumina (AD90) and a silicon carbide whisker-reinforced alumina composite (Al₂O₃-SiC_w) at room temperature in air using a combined loading technique for stabilizing crack growth, and a surface film technique for monitoring crack length. Fatigue crack growth was evaluated successfully with those experimental techniques. Load shedding tests were performed until the crack became dormant, in order to determine the threshold stress intensity factor K_th. Subsequently, the specimens were used for quasi-static crack growth tests under a monotonic loading condition. The R-curves were determined in this experiment; however, fracture resistance did not increase markedly with crack growth. Detailed observations of the crack growth behaviour revealed that the flat R-curve was attributed to the shielding effect of the fatigue crack tip wake. Thus, the fatigue precrack introduced by the load shedding test was not regarded as an ideal crack for determining the R-curve. Fractographic observations were performed to investigate the mechanistic difference between fatigue and quasi-static crack growth. It was found that the cyclic loading produced fretting damage in the wake region and it reduced the shielding effect of the fatigue cracks. Based on the experimental results, the relationship between the fatigue crack growth and the R-curve is discussed as is the significance of K_th as a material parameter.     

Fracture criterion for kinking cracks in a tri-material adhesively bonded joint under mixed mode loading

The fracture behavior of a composite/adhesive/steel bonded joint was investigated by using double cantilever beam specimens. A starter crack is embedded at the steel/adhesive interface by inserting Teflon tape. The composite adherend is a random carbon fiber reinforced vinyl ester resin composite while the other adherend is cold rolled steel. The adhesive is a one-part epoxy that is heat cured. The Fernlund-Spelt mixed mode loading fixture was employed to generate five different mode mixities. Due to the dissimilar adherends, crack turning into the adhesive (or crack kinking) associated with joint failure, was observed. The bulk fracture toughness of the adhesive was measured separately by using standard compact tension specimens. The strain energy release rates for kinking cracks at the critical loads were calculated by a commercial finite element analysis software ABAQUS in conjunction with the virtual crack closure technique. Two fracture criteria related to strain energy release rates were examined. These are (1) maximum energy release rate criterion (G_max) and, (2) mode I facture criterion (G_II = 0). They are shown to be equivalent in this study. That is, crack kinking takes place at the angle close to maximum G or G_I (also minimum G_II, with a value that is approximately zero). The average value of G_IC obtained from bulk adhesive tests using compact tension specimens is shown to be an accurate indicator of the mode I fracture toughness of the kinking cracks within the adhesive layer. It is concluded that the crack in tri-material adhesively bonded joint tends to initiate into the adhesive along a path that promotes failure in pure mode I, locally.     

CRACK FACE INTERACTIONS AND NEAR-THRESHOLD FATIGUE CRACK GROWTH

Rough fracture surfaces usually influence substantially the fatigue growth properties of materials in the regime of low growth rates. Friction, abrasion, interlocking of fracture surface asperites and fretting debris reduce the applied load amplitude to a smaller effective value at the crack tip (“sliding crack closure”, or “crack surface interaction” or “crack surface interference”). The influence of these phenomena on the fatigue crack growth properties of structural steel is discussed and compared for the two kinds of mixed mode loading employed in this work. Mixed mode loading was performed by (A): cyclic mode III + superimposed static mode I and (B): cyclic mode I + superimposed static mode III loading. Such loading cases frequently occur in rotating load-transmission devices. Several differences are typical for these two mixed-mode loading cases. A superimposed static mode I load increases the crack propagation rate under cyclic mode III loading whereas cyclic mode I fatigue crack propagation is retarded when a static mode III load is superimposed. Increase of the R -ratio (of the cyclic mode III load) leads to an insignificant increase of fracture surface interaction and subsequently to a small decrease of the crack growth rate for cyclic mode III loading, whereas higher R -values during cyclic mode I+ superimposed static mode III loading lead to a significant reduction of the crack growth rates.     

Mechanical property and R-curve behavior of the B4C/BN ceramics composites

The B₄C/BN ceramics composites were fabricated by the hot-pressing process. In this paper, the mechanical property and R-curves behavior of the B₄C/BN composites were investigated. The fracture strength and fracture toughness of the B₄C/BN microcomposites and the B₄C/BN nanocomposites decreased gradually with the increasing content of h-BN. The fracture strength and fracture toughness of the B₄C/BN nanocomposites were significantly improved in comparison with the B₄C/BN microcomposites. The damage resistance and R-curves behavior of the B₄C monolith and the B₄C/BN composites were evaluated by the indentation-strength in bending technique (ISB). The fracture strength of the B₄C monolith, the B₄C/BN microcomposites and the B₄C/BN nanocomposites decreased gradually with the increase of the indentation load. The B₄C/BN nanocomposites retained relative higher fracture strength in comparison with the B₄C monolith and the B₄C/BN microcomposites under the equivalent indentation load. The B₄C monolith, the B₄C/BN microcomposites and the B₄C/BN nanocomposites all exhibited the rising R-curves behavior. The B₄C/BN nanocomposites exhibited the higher rising R-curve behavior than that of the B₄C monolith and the B₄C/BN microcomposites. The toughness mechanisms of the composites were investigated. The B₄C/BN composites with the h-BN content more than 20 wt.% exhibited excellent machinability. The slowly rising R-curves behavior remarkably improved the machinability of the composites.