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Theoretical and experimental comparisons of the nonlinear energy method to the J-integral, R-curve and COD methods in fracture toughness testing

Because of the current high degree of interest in the development of a standard nonlinear test method, analytical and experimental comparisons have been made between the R-curve, COD, J-integral and nonlinear energy methods. A general definition of fracture toughness is proposed and the fundamental definitions of each method are compared to it. Experimental comparisons between the COD, J-integral, nonlinear energy and standard ASTM methods have been made for a series of compact tension tests on several aluminum alloys. Some of the tests were conducted according to the ASTM standard method E399-72, while the specimen thickness was reduced below the minimum requirement for plane strain fracture toughness testing for several other test series. The fracture toughness values obtained by the COD method were significantly higher than the toughness values obtained by the other three methods. All of the methods displayed a tendency to yield higher toughness values as the thickness was decreased below the ASTM plane strain requirement.

Liebowitz, H.↗

Comparisons of various configurations of the edge delamination test for interlaminar fracture toughness

Various configurations of Edge Delamination Tension (EDT) test specimens, of both brittle (T300/5208) and toughened-matrix (T300/BP907) graphite reinforced composite laminates, were manufactured and tested. The mixed-mode interlaminar fracture toughness, G sub C, was measured using (30/30 sub 2/30/90 sub N)sub s, n=1 or 2, (35/-35/0/90) sub s and (35/0/-35/90) sub s layups designed to delaminate at low tensile strains. Laminates were made without inserts so that delaminations would form naturally between the central 90 deg plies and the adjacent angle plies. Laminates were also made with Teflon inserts implanted between the 90 deg plies and the adjacent angle (theta) plies at the straight edge to obtain a planar fracture surface. In addition, interlaminar tension fracture toughness, GIc, was measured from laminates with the same layup but with inserts in the midplane, between the central 90 deg plies, at the straight edge. All of the EDT configurations were useful for ranking the delamination resistance of composites with different matrix resins. Furthermore, the variety of layups and configurations available yield interlaminar fracture toughness measurements needed to generate delamination failure criteria. The influence of insert thickness and location, and coupon size on G sub c values were evaluated.

Obrien, T. K.↗

Interlaminar fracture toughness: Three-dimensional finite element modeling for end-notch and mixed-mode flexure

A computational procedure is described for evaluating End-Notch-Flexure (ENF) and Mixed-Mode-Flexure (MMF) interlaminar fracture toughness in unidirectional fiber composites. The procedure consists of a three-dimensional finite element analysis in conjunction with the strain energy release rate concept and with composite micromechanics. The procedure is used to analyze select cases of ENF and MMF. The strain energy release rate predicted by this procedure is in good agreement with limited experimental data. The procedure is used to identify significant parameters associated with interlaminar fracture toughness. It is also used to determine the critical strain energy release rate and its attendant crack length in ENF and/or MMF. This computational procedure has considerable versatility/generality and provides extensive information about interlaminar fracture toughness in fiber composites.

Murthy, P. L. N.↗

Strength, Fracture Toughness, and Slow Crack Growth of Zirconia/alumina Composites at Elevated Temperature

Various electrolyte materials for solid oxide fuel cells were fabricated by hot pressing 10 mol% yttria-stabilized zirconia (10-YSZ) reinforced with two different forms of alumina particulates and platelets each containing 0 to 30 mol% alumina. Flexure strength and fracture toughness of platelet composites were determined as a function of alumina content at 1000 C in air and compared with those of particulate composites determined previously. In general, elevated-temperature strength and fracture toughness of both composite systems increased with increasing alumina content. For a given alumina content, flexure strength of particulate composites was greater than that of platelet composites at higher alumina contents (greater than or equal to 20 mol%), whereas, fracture toughness was greater in platelet composites than in particulate composites, regardless of alumina content. The results of slow crack growth (SCG) testing, determined at 1000 C via dynamic fatigue testing for three different composites including 0 mol% (10-YSZ matrix), 30 mol % particulate and 30 mol% platelet composites, showed that susceptibility to SCG was greatest with SCG parameter n = 6 to 8 for both 0 and 30 mol% particulate composites and was least with n = 33 for the 30 mol% platelet composite.

Choi, Sung R.↗

Effect of Specimen Thickness on Fracture Toughness and Plane Stress to Plane Strain Transition in Medium-Density Polyethylene

This study investigates the effect of specimen thickness on fracture toughness and the transition from plane stress to plane strain conditions in Medium-Density Polyethylene (MDPE) using Single Edge Notched Bend (SENB) specimens. Three thickness groups (7.5 mm, 9.0 mm, and 12.1 mm) were tested following ASTM D5045 protocol. Conditional stress intensity factors (KQ) increased from 2.2 MPavm to 2.8 MPavm with increasing thickness, demonstrating significant size dependency. Confocal microscopy revealed a 34% reduction in maximum crack tip opening displacement (CTOD) from 0.478 mm to 0.314 mm as thickness increased, with plastic zone lateral extent decreasing by 32%. This quantitative evidence validates Irwin's theoretical prediction of plastic zone size transition from plane stress r_y˜ (1/2p) (K_I/s_y )^2 to plane strain conditions r_y˜ (1/6p) (K_I/s_y )^2.Scanning electron microscopy confirmed progressive suppression of shear lips and evolution from ductile tearing with extensive polymer chain drawing in thin specimens to localized crazing in thick specimens. Despite all specimens satisfying the ASTM D5045 criterion (B = 2.5(KQ/s_y )^2 ) ,residual shear lips persisted even in the thickest specimens, demonstrating that nominal size requirements alone are insufficient for achieving complete plane strain conditions in highly ductile polymers. The findings emphasize the necessity of integrated analytical and morphological assessment for valid fracture toughness characterization, with critical implications for life assessment and integrity prediction in thick-section polymer components such as natural gas distribution pipelines.

Medium-Density Polyethylene↗

Fracture toughness of hot-pressed beryllium

This paper presents the results of an investigation into the fracture toughness, sustained-load flaw growth, and fatigue-crack propagation resistance of S200E hot-pressed beryllium at room temperature. It also reviews the literature pertaining to the influence of various factors on the fracture toughness of hot-pressed beryllium determined using fatigue-cracked specimens.

Lemon, D. D.↗

Effect of fiber orientation on the fracture toughness of brittle matrix composites

The effective fracture toughness of brittle matrix materials can be increased through the addition of short, poorly bonded fibers which bridge the growing crack. The orientation distribution of the fibers is likely to be biased, and not in an ideal random or aligned state. A micromechanical model is formulated for the postcracking behavior using the force-displacement relation for an arbitrary fiber bridging a crack, the fiber orientation density function, and the fiber location density function. This model is then used to determine an effective traction law for the bridging fibers, as well as the steady state bridging toughness increment. In most cases, the results may be placed in the form of a product of the aligned fiber results times a modifying integrated orientation factor. The frictional shear stress on fiber pull-out is allowed to vary during pull-out, modeling the effects of matrix breakdown, fiber surface smoothing or wear debris accumulation. Results are presented for a variety of representative planar and three-dimensional fiber orientation states.

Jain, L. K.↗

Heavy section fracture toughness screening specimen

Size requirements for a pin loaded double edge notch + crack tension specimen proposed for fracture toughness screening heavy section alloys were studied. Ranking of eight selected alloys based on the specimen's net strength was compared with that based on the valid plane strain fracture toughness separately determined. Performance of the specimen was judged on the basis of that comparison. The specimen's net strength was influenced by three critical specimen dimensions: distance between the crack plane and the loading hole, specimen width, and specimen thickness. Interaction between the stress fields of the crack and the loading holes reduced the net strength, but this effect disappeared as the separation reached a dimension equal to the specimen width. The effects of specimen width and thickness are interrelated and affect the net strength through their influence on the development of the crack tip plastic zone.

Shannon, J. L., Jr.↗

Effects of aging condition on the fracture toughness of 2XXX and 7XXX series aluminum alloy composites

Results are presented on the effects of matrix aging condition (i.e., matrix temper) on the fracture toughness of 2XXX and 7XXX Al matrix alloys reinforced with SiC particulates, and the results are compared with the mechanical behavior. Fracture toughness testing was conducted on fatigue precracked bend specimens, and fracture surfaces were examined using SEM. Results revealed dramatic differences in the effect of matrix microstructure on the fracture properties of the two composite series. In the 7XXX material, the toughness values decreased from the underaged (UA) condition to the overaged (OA) condition by approximately 40 percent, while in the 2XXX series composite, the effect of matrix microstructure was marginal. In the 7XXX series composites, a transition in fracture mode from particle cracking (in UA) to matrix and linear-interface failure (in OA) was observed, while the 2XXX series composite failed predominantly by particle cracking.

Manoharan, M.↗

Aging effects on the fracture toughness of SiC whisker reinforced 2XXX aluminum alloys

The effect of aging (at 150 C) time on the fracture toughness behavior of a 2XXX alloy (Al-3.55Cu-1.29Mg-0.01Fe-trace Mn) reinforced with 5 vol pct F-8 SiC whiskers was investigated by measuring hardness and electrical conductivity followed by fracture toughness tests on center-cracked specimens. The ageing time-hardening response plots showed that, independent of whisker orientation, the initial rapid increase in hardness was followed by a more gradual increase, with a broad hardness peak between 32 and 128 hrs of aging. Coincident with the hardness changes, the electrical conductivity initially decreased, reached a minimum, and then increased at aging times beyond 32 hrs. Examination by SEM indicated that the initial increase in hardness and decrease in conductivity was due to the GPB zone formation, while the subsequent increase in electrical conductivity and decrease in hardness (overaging) was due to S nucleation and growth.

Ratnaparkhi, P. L.↗

Increased fracture toughness of graphite-epoxy composites through intermittent interlaminar bonding

The objective of this study was to increase the fracture toughness of multilayer continuous-filament graphite-epoxy composites. The method used is intermittent interlaminar bonding which can lead to a large increase in the fracture surface area. Intermittent bonding was achieved through introduction of thin perforated Mylar between the layers of the composite. For the optimum condition, fracture toughness was increased from about 100 kJ/sq m for untreated specimens to an average of about 500 kJ/sq m, while tensile strength dropped from 500 MPa to 400 MPa, and elastic modulus remained the same at about 75 GPa. An approximate analysis is presented to explain the improvement in toughness.

Jea, L.-C.↗

Fracture toughness computational simulation of general delaminations in fiber composites

A procedure is described to computationally simulate composite laminate fracture toughness in terms of strain energy release rate. It is also used to evaluate the degradation in laminate structural integrity in terms of displacements, loss in stiffness, loss in vibration frequencies and loss in buckling resistance. Specific laminates are selected for detail studies in order to demonstrate the generality of the procedure. These laminates had center delaminations, off-center delaminations, and pocket delaminations (center and off-center) at the free-edge and center delaminations at the interior. The laminates had two different thicknesses and were made from three different materials. The results obtained are presented in graphical form to illustrate the effects of delamination on the laminate structural integrity and on the laminate strain energy release rate (composite fracture toughness).

Wilt, T. E.↗

An investigation of fracture toughness, fatigue-crack growth, sustained-load flaw growth, and impact properties of three pressure vessel steels

The elastic fracture toughness of the three steels is shown to not decrease significantly with decreasing temperature from room temperature to about 244 K (-20 F.). The elastic fracture toughness of the three steels increased with increasing specimen width and thickness. The fatigue-crack-growth data for all three steels fall into relatively narrow scatter bands on plots of rate against stress-intensity range. An equation is shown to predict the upper bounds of the scatter bands reasonably well. Charpy impact energies decreased with decreasing temperature in the nominal temperature range from room temperature to 244 K (-20 F). The nil-ductility temperatures of the steels are discussed.

Hudson, C. M.↗

Fracture toughness computational simulation of general delaminations in fiber composites

A procedure is described to computationally simulate composite laminate fracture toughness in terms of strain energy release rate (SERR). It is also used to evaluate the degradation in laminate structural integrity in terms of displacements, loss in stiffness, loss in vibration frequencies and loss in buckling resistance. Specific laminates are selected for detail studies in order to demonstrate the generality of the procedure. These laminates had center delaminations, off-center delaminations, and pocket delaminations (center and off-center) at the free-edge and center delaminations at the interior. The laminates had two different thicknesses and were made from three different materials. The results obtained are presented in graphical form to illustrate the effects of delamination on the laminate structural integrity and on the laminate strain energy release rate (composite fracture toughness).

Murthy, P. L. N.↗

Effect of minor reactive metal additions on fracture toughness of iron: 12-percent nickel alloy at-196 deg and 25 deg C

The slow bend precracked Charpy fracture toughness and tensile behavior of arc-melted and hot-rolled Fe-12Ni alloys containing up to 4 atomic percent reactive metal additions were determined at -196 C and 25 C after water quenching from three annealing temperatures. The fracture toughness of Fe-12Ni at -196 C was improved by small amounts of Al, Ce, Hf, La, Nb, Ta, Ti, V, Y, and Zr, but not by Si. Cryogenic toughness was improved up to 7.5 times that of binary Fe-12Ni and varied with the reactive metal, its concentration, and the annealing temperature.

Witzke, W. R.↗

Composite Interlaminar Shear Fracture Toughness, G(sub 2c): Shear Measurement of Sheer Myth?

The concept of G2c as a measure of the interlaminar shear fracture toughness of a composite material is critically examined. In particular, it is argued that the apparent G2c as typically measured is inconsistent with the original definition of shear fracture. It is shown that interlaminar shear failure actually consists of tension failures in the resin rich layers between plies followed by the coalescence of ligaments created by these failures and not the sliding of two planes relative to one another that is assumed in fracture mechanics theory. Several strain energy release rate solutions are reviewed for delamination in composite laminates and structural components where failures have been experimentally documented. Failures typically occur at a location where the mode 1 component accounts for at least one half of the total G at failure. Hence, it is the mode I and mixed-mode interlaminar fracture toughness data that will be most useful in predicting delamination failure in composite components in service. Although apparent G2c measurements may prove useful for completeness of generating mixed-mode criteria, the accuracy of these measurements may have very little influence on the prediction of mixed-mode failures in most structural components.

OBrien, T. Kevin↗

Survey of fracture toughness test methods

Comprehensive survey presents current methods of fracture toughness testing that are based on linear elastic fracture mechanics. General principles of the basic two dimensional crack stress field model are discussed in relation to real three dimensional specimens. Methods of test instrumentation and procedure are described.

Brown, W. F., Jr.↗