Mixed mode fracture

Other researchers have substantially advanced the state of the art of fracture mechanics applied to composite materials. Tetelman [6-15] and Corten [6-16] discuss fracture mechanics from the point of view of micromechanics. Sih and Chen [6-17] treat the mixed-mode fracture problem for noncollinear crack propagation. Waddoups, Eisenmann, and Kaminski [6-18] and Konish, Swedlow, and Cruse [6-19] extend the concepts of fracture mechanics to laminates. Impact resistance of unidirectional composites is discussed by Chamis, Hanson, and Serafini [6-20]. They use strain energy and fracture strength concepts along with micromechanics to assess impact resistance in longitudinal, transverse, and shear modes. 

Fig. 3.33. CLS specimen for mixed mode interlaminar fracture tests.

Russell, A.J. and Street, K.N. (1985). Moisture and temperature effects on the mixed-mode delamination fracture of unidirectional graphite/epoxy. In Delamination and Debonding of Materials, ASTM STP 876 (W.S. Johnson ed.), ASTM, Philadelphia, PA, pp. 349-372. 

Singh, S. and Partridge, l.K. (1995). Mixed mode fracture in an interleaved carbon fiber-epoxy composite. Composites Set. Tecimof 55. 319-327. 

T. Nishioka and S. N. Atluri, Path-Independent Integrals, Energy Release Rates, and General Solutions of Near-Tip Fields in Mixed-Mode Dynamic Fracture Mechanics, Engineering Fracture Mechanics, 18, 1-22 (1983). 

Block polymer B differs substantially in its failure characteristics from BP A polycarbonate. For the block polymer a mixed failure mode predominates in three-point bend tests of notched specimens from —100°-90°C. In the mixed mode craze breakdown and plane strain fracture occur first inside the specimen subsequently shear failure occurs in the surface regions of the specimen. Shear lips (11) are formed as a result. Shear lips are also found on the notched Izod impact fracture surfaces of block polymer B, implying that the same mixed mode of failure occurs under high speed loading conditions. 

Fig. 37. Fatigue fracture diagram for PEI at 10 Hz, R = O.J, showing the regions of crazK and mixed mode dominated crack growth...

In PEI (Fig. 37), the shear fracture process never fully develops (under the tested conditions). A mixed mode develops, with some elements of shear fracture, but without the epsilon plane strain shear bands, a true 45° shear fracture process cannot develop. The lifetime enhancement is not as substantial, as seen in PC and PEC. 

This paper presents results from a study of assemblies composed of glass fibre reinforced epoxy composites. First, tests performed to produce mixed mode fracture envelopes are presented. Then results from tests on lap shear and L-stiffener specimens are given. These enabled failure mechanisms to be examined in more detail using an image analysis technique to quantify local strain fields. Finally the application of a fracture-mechanics-based analysis to predict the failure loads of top-hat stiffeners with and without implanted bond-line defects is described. Correlation between test results and predictions is reasonable, but special attention is needed to account for size effects and micro-structural variations induced by the assembly process. 

The paper is presented in three parts. First, the tests employed to determine the mixed mode fracture envelope of a glass fibre reinforced epoxy composite adhesively bonded with either a brittle or a ductile adhesive are briefly described. These include mode I (DCB), and mixed mode (MMB) with various mixed mode (I/II) ratios. In the second part of the paper different structural joints will be discussed. These include single and double lap shear and L-specimens. In a recent European thematic network lap shear and double lap shear composite joints were tested, and predictions of failure load were made by different academic and industrial partners [9,10]. It was apparent that considerable differences existed between different analytical predictions and FE analyses, and correlation with tests proved complex. In particular, the progressive damage development in assemblies bonded with a ductile adhesive was not treated adequately. A more detailed study of damage mechanisms was therefore undertaken, using image analysis combined with microscopy to examine the crack tip strain fields and measure adherend displacements. This is described below and correlation is made between predicted displacements and failure loads, based on the mixed mode envelope determined previously, and measured values. 

Fracture mechanics characterisation tests have been performed to determine the mixed mode fracture envelope of an epoxy bonded glass/epoxy composite. Analysis of lap shear, and L-stiffener geometries has shown that for this relatively brittle adhesive reasonable first estimations of failure loads can be obtained for both cracked and uncracked specimens. An image analysis technique has been developed which enables failure mechanisms to be... 

Hashemi S, Kinloch AJ, Williams G, Mixed mode fracture in fiber-polymer composite laminates, ASTM STP 1110, ed O Brien TK, 1991, 143-168. 

Concrete structure. Retrofitting, Carbon fiber sheet. Adhesive interface, Mixed mode. Fracture toughness. Fracture criterion... 

In the present work, a novel experimental method was proposed to evaluate the modes I-fll fracture toughness of the adhesive interface between concrete and carbon fiber sheets. The validity of the evaluation formula was studied on the basis of the results of finite element analysis. The mixed mode fracture toughness and fracture criterion of the adhesive interface were also studied on the basis of the results of fracture toughness test using the proposed method. 

The MMD (Mixed Mode Disk) specimen was proposed to investigate the modes I+II fracture behavior of the adhesive interface between concrete and carbon fiber sheets. This specimen, which consists of two concrete blocks inserted carbon fiber sheets and steel jigs, is basically similar to the Arcan specimen, as shown in Fig. 3 [12]. However, the evaluation formula for the Arcan specimen can not be directly applied to the MMD specimen owing to the difference of geometries and the existence of carbon fiber sheets. For the present specimen, the adhesive region was set to be smaller than the face of... 

Fig. 12. Experimental apparatus of the mixed mode fracture toughness test.

The mixed mode fracture toughness tests were carried out on a universal testing machine at loading rate of 1 mm/min. The loading angle was varied to study the criterion of mixed mode fracture as = 0°, 15°, 30°, 90° (G /G=0.01, 0.31, 0.55, 0.95). 

Fig. 14. Macroscopic fracture morphology of the mixed mode disk specimen.

Figure 15 shows the diagram of the mixed mode fracture toughness, G. The abscissa shows the mode I component of the mixed mode energy release rate, G[. The ordinate shows the mode II component of the mixed mode energy release rate, G[j. Each plot is the average value of 5-10 test data. 

Fig. 15. Mixed mode fracture toughness of the adhesive interface between concrete and carbon fiber sheets each plot is the average value of 5-10 test data.

In addition, the fracture toughness, G, of the present specimen was much lower than that of the adhesive resin itself This would be also the consequence that the microscopic fracture occurred in the concrete blocks. However, the mixed mode fracture toughness, G, approximately coincided with the linear fracture criterion, G,+ G = const., [17]. This result suggests that the principle of superposition was valid for the present specimen, which is very important conclusion for the structural design. 

In order to apply the characterization and structural design of the concrete bridge structures retrofitted with tensioned carbon fiber sheets, the mixed mode disk specimen was proposed and applied to the mixed mode fracture toughness tests. The following conclusions were derived from the results and discussions ... 

The mixed mode fracture toughness of the acrylic resin adhesive interface was obtained by applying the proposed method. The mode II fracture toughness was more than twiee as high as the mode I fracture toughness. 

The mixed mode fracture toughness of the adhesive interface followed the linear fracture criterion. This result suggests that the principle of superposition was valid... 

Choi, N.S., Kinloch, A.J., Williams, J.G., (1999) Delamination Fracture of Multidirectional Carbon-Fiber/Epoxy Composites under Mode I, Mode II and Mixed Mode I/II Loading , / Comp. Mat. 33, No.l, pp. 73-100. 

Edited by K J. Miller and E.R. de los Rios ESIS 14 Mixed Mode Fatigue and Fracture... 

For obvious reasons, fr ture mechanics studies have concentrated on opening mode (Mode 1) fractures, and only a few studies have been made of other fracture modes. In one such study, Bascom etaL performed mixed-mode fracture tests on epoxy resin adhesives, vnth the epoxy layer at 45° to the applied stress . This test combines the opening Mode I widi die in-idaiK shear Mode II. The authors calculated a mixed-mode fracture etffirgy G/ jjc from the results, and obtained a... 

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