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At least 73 records · Page 4

A Cohesive Element Formulation for Simulation of General Mode I, II and III Delamination

Cohesive element formulations proposed thus far have assumed that Mode II and Mode III fracture processes, and hence traction-separation laws, are identical. However, experimental observations suggest that such an assumption may not hold in general. The approach described herein consists of a cohesive element formulation in which the assumption of identical Mode II and Mode III fracture processes is not required. This assumption is alleviated by estimating the normal to the delamination front based on the gradient of the displacement jumps determined within each element. The estimated normal is used to rotate the cohesive element coordinate system. Determining the displacement jumps in the rotated coordinate system enables the distinction between Mode II sliding, and Mode III tearing. This information is subsequently used to extend a recently proposed cohesive formulation, resulting in an approach that can simulate mixed-mode I/II/III fracture via prescribing piecewise-linear traction-separation laws combined with a 3D mixed-mode fracture criteria.

Delamination↗

Configurational stability of a crack propagating in a material with mode-dependent fracture energy – Part II: Drift of fracture facets in mixed-mode I+II+III

In earlier papers (Leblond et al., 2011; 2019), we presented linear stability analyses of the coplanar propagation of a crack loaded in mixed-mode I+III, based on a “double” propagation criterion combining (Griffith, 1920)’s energetic condition and (Goldstein and Salganik, 1974)’s principle of local symmetry. The difference between the two papers was that in the more recent one, the local value of the critical energy-release-rate was no longer considered as a constant, but heuristically allowed to depend upon the ratio of the local mode III to mode I stress intensity factors. This led to a much improved, qualitatively acceptable agreement of theory and experiments, for the “threshold” value of the ratio of the unperturbed mode III to mode I stress intensity factors, above which coplanar propagation becomes unstable. In this paper, the analysis is extended to the case where a small additional mode II loading component is present in the initially planar configuration of the crack, generating a small, general kink of this crack from the moment it is applied. The main new effect resulting from presence of such a loading component is that the instability modes present above the threshold must drift along the crack front during its propagation. This prediction may be useful for future theoretical interpretations of a number of experiments where such a drifting motion was indeed observed.

36 MATERIALS SCIENCE↗

The effect of mixed mode precracking on the mode 1 fracture toughness of composite laminates

We subjected double cantilever beam specimens from four different composite materials to mixed-mode precracking. Three different precracking mode 1 to mode 2 ratios were used--1 to 4, 1 to 1, and 4 to 1. Following precracking the specimens were tested for mode I fracture toughness. The mixed-mode precracking often influenced the mode 1 toughness and its influence persisted for as much as 60 mm of mode 1 crack growth. We tested composites with untoughened matrices, composites with rubber-toughened matrices, and composites with interlayer toughening. Depending on material type and precracking mode ratio, the precracking could cause either a significant increase or a significant decrease in the mode 1 fracture toughness.

Shankar, Prashanth↗

Calculating Mode Mixity in Interlaminar Fracture of Composite Laminates

To accurately predict delamination under mixed-mode loading, cohesive elements must partition the energies dissipated in Mode I and Mode II correctly. The ability of cohesive models to predict mode mixity was evaluated by performing analyses of the single leg bending (SLB) test, which exhibits a variable mode mixity with crack length. Accordingly, two numerical integration methods were developed to compute the energy partitioning: (i) a local calculation of the accumulated work of tractions at each point along the crack path, and (ii) a global J-integral “snapshot” calculation along a contour around the process zone. In the case of a composite laminate with properties characterized by short fracture process zone (FPZ), the results of these two methods correlate well with each other and with a linear elastic fracture mechanics solution. However, FPZscan be long due to fiber bridging or due to the intrinsic toughness of the material. Then, the results of mode-mixity calculations obtained with various methods vary widely from each other. It is argued that the global J-integral calculation is the most accurate interpretation of the energy release rate and mode mixity for either short or long process zones. This solution will provide a more accurate characterization of resistance curves and mode mixity in experimental results, and it will also guide the development of more accurate mixed-mode cohesive laws for tougher materials characterized by strong R-curve responses, such as thermo-plastic composites.

cohesive zone analysis↗

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↗

Determination of interlaminar fracture toughness and fracture mode dependence of composites using the edge delamination test

Edge delamination testing has been conducted in order to determine the mixed mode interlaminar fracture toughness of unnotched (+, -35/0/90)s and (0/+, -35/90)s laminates with graphite fibers and epoxy matrices, with or without elastomer additives. Although the two stacking sequences were chosen so that the total strain energy release rates were equal, the percentages of crack opening and shear mode energy release rates were found to vary widely between the layups. Plots of interlaminar fracture toughness as a function of crack opening energy release rate percentage have been drawn to generate delamination failure criteria which reflect the observed fracture mode dependence.

Obrien, T. K.↗

Interlaminar fracture toughness of composites. II - Refinement of the edge delamination test and application to thermoplastics

The mixed mode interlaminar fracture toughness, G(c), is obtained for the two thermoplastic matrices UDEL P1700 polysulfone and ULTEM polyetherimide by means of edge delamination tensile (EDT) tests on unnotched, eleven-ply graphite fiber reinforced composite specimens. A novel method is used to obtain the stiffness parameter employed in the closed form equation for the calculation of G(c), decreasing the number of stiffness measurements required and simplifying the calculations. The G(Ic) values from double cantilever beam (DCB) measurements on composites of the two thermoplastics were similar to each other, but slightly higher than the G(c) data obtained by EDT. Interfacial resin/fiber failures predominated in both the EDT and DCB tests.

Johnston, N. J.↗

Fracture toughness evaluations for spent nuclear fuel dry storage canister welds and spent nuclear fuel clad-pellet structures

Integrity of spent nuclear fuel (SNF) interim storage canisters is very important to the safety of the back-end nuclear fuel cycle. Stress corrosion cracking (SCC) potential of interim storage canister has been considered as a high priority. Because no post-weld heat treatment was required for forming these canisters, the high tensile residual stress existed within these canister welds. This can change the fracture resistance capacity significantly as well as increase SCC potential. Due to relative thin shell thickness of a canister weldment, the spiral notch torsion test (SNTT) method was used to estimate the canister weldment fracture toughness. SNTT was developed to measure the intrinsic fracture toughness of structural materials using small specimens. The SNTT method has been applied to a wide variety of structural materials, such as low-alloy steels, stainless steel, aluminum alloy, ceramics, concrete, and composites. The SNTT system operates by applying pure torsion to cylindrical specimens with a notch line that spirals around the specimen at a 45° pitch. In order to carry out pure torsion load mode, biaxial tension/torsion tester was developed accordingly to perform SNTT protocol. Moreover, applying fracture mechanics approach to SNF system reliability investigation is warranted due to the inherent flaws and hydride structures existed in a SNF system after nuclear reactor operation. However, none of the existing fracture toughness data deal with fuel cladding specific geometry or spent fuel material conditions, such as cladding structure with the pellet-inserts and the associated pellet clad mechanical interactions induced mixed-mode damage mechanisms. Thus, the development of an intrinsic fracture mechanics approach that is suitable for SNF materials is needed. Furthermore, due to thin wall and small dimension of clad tubing structure, the SNTT method was used to estimate the clad tubing structure fracture toughness. Fracture testing were performed on the received stainless steel canister weldment, most SNTT weld samples fracture initiation sites are at heat-affected zone (HAZ) regions. The estimated fracture toughness J Q ’ for the baseline SS304 steel is at 283 kJ/m². The estimated JQ’ for the SS304/308 weld and baseline metals are 148 kJ/m 2 and 459 kJ/m 2 , respectively. Out of cell fracture testing for spent fuel structure were carried out on the surrogate rods made of Zr-4 clad and alumina inserts, the estimated fracture toughness values for baseline Zr-4 cladding with alumina-pellet inserts are: (1) For SNTT samples with a short or medium crack length, between 5.4-mm and 8-mm, the estimate J IQ upon fracture initiation for the baseline Zr-4 cladding is at 50 kJ/m 2 with 2-sigma uncertainty of 3.26 kJ/m 2 , and the associated K IQ is at 67.46 MPa$\sqrt{m}$; and (2) For SNTT samples with a long crack length, around 13-mm, the crack initialization is deviated from that of the Mode-I tensile fracture and appears to be a mixed-mode fracture of Mode I - tensile stress and Mode III - out of plane shear stress; the estimated J MQ is at 18.9 kJ/m 2 , the associated K MQ is at 41.4 MPa$\sqrt{m}$.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

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.↗

Fracture toughness evaluation for Zr-4 clad tubing structure with pellet inserts

Applying fracture mechanics approach to spent nuclear fuel (SNF) system reliability investigation is warranted due to the inherent flaws and hydride structures existed in a SNF system after nuclear reactor operation. However, none of the existing fracture toughness data deal with fuel cladding specific geometry or spent fuel material conditions, such as cladding structure with the pellet-inserts and the associated pellet clad mechanical interactions induced mixed-mode damage mechanisms. Thus, the development of an intrinsic fracture mechanics approach that is suitable for SNF materials is needed. Due to thin wall and small dimension of clad tubing structure, the spiral notch torsion test (SNTT) method of small specimen approach was used to estimate the clad tubing structure fracture toughness. The estimated fracture toughness for Zr-4 cladding with alumina-pellet inserts are presented in this report. For SNTT samples with a short or medium crack length, between 5.4-mm and 8-mm, the estimate JIQ upon fracture initiation for the baseline Zr-4 cladding is at 50 kJ/m2 with 2-sigma uncertainty of 3.26 kJ/m2, and the associated KIQ is at 67.46 MPa√m. For SNTT samples with a long crack length, around 13-mm, the crack initialization is deviated from that of the Mode-I tensile fracture and appears to be a mixed-mode fracture of Mode I – tensile stress and Mode III – out of plane shear stress; the estimated JMQ is at 18.9 kJ/m2, the associated KMQ is at 41.4 MPa√m.

36 MATERIALS SCIENCE↗

Fracture toughness of polycrystalline ceramics in combined mode I and mode II loading

The present investigation of the fracture of alumina and zirconia polycrystalline ceramic specimens of precracked-disk type, in diametral compression, evaluated fracture toughness in pure mode I, combined mode I/mode II, and pure mode II, depending on the alignment of the center crack relative to the loading diameter. The mixed-mode fracture-toughness envelope thus obtained exhibits significant deviation to higher fracture toughness in mode II, relative to the predictions of linear elastic fracture mechanics theory. Crack-surface resistance due to grain-interlocking and abrasion are identified as the primary sources of increased fracture resistance in mode II loading of the polycrystalline ceramics.

Singh, Dileep↗

Delamination and debonding of materials

The general topics consist of stress analysis, mechanical behavior, and fractography/NDI of composite laminates. Papers are presented on a dynamic hybrid finite-element analysis for interfacial cracks in composites, energy release rate during delamination crack growth in composite laminates, matrix deformation and fracture in graphite-reinforced epoxies, and the role of delamination and damage development on the strength of thick notched laminates. In addition, consideration is given to a new ply model for interlaminar stress analysis, a fracture mechanics approach for designing adhesively bonded joints, the analysis of local delaminations and their influence on composite laminate behavior, and moisture and temperature effects on the mixed-mode delamination fracture of unidirectional graphite/epoxy.

Johnson, W. S.↗

Preliminary design of cracked-lap shear specimen thickness for determination of interlaminar fracture toughness

This paper outlines a technique for preliminary sizing of the adherends for cracked-lap-shear specimen to assure delamination instead of adherend failure. The cracked-lap-shear specimen is a popular specimen used for determination of mixed mode interlaminar fracture toughness of composites. Thin adherends, on the order of three plies thick, have been used successfully in the past for determination of fracture toughness of rather brittle matrix systems. However, the tougher matrices now being considered for composite applications require thicker adherends in order to get composite delamination rather than adherend failure. The optimum thickness is obtained on the basis that the critical value of the strain energy release rate is reached at the delamination front before the ultimate strength is reached in the adherend. By proper design the specimen would delaminate and not use excessive material or load. A simple analysis for the optimum adherend thickness and experimental verification are included.

Mangalgiri, P. D.↗

The effect of loading direction on the fracture behaviors of cortical bone at a dynamic loading rate

Here, the dynamic cracking processes in porcine cortical bone were visualized in real-time using the high-speed synchrotron X-ray phase-contrast imaging (PCI) technique in three osteon orientations: in-plane transverse, out-of-plane transverse and in-plane longitudinal. The dynamic flexural loading applied on the pre-notched bone specimens was introduced by a modified Kolsky compression bar. High-speed X-ray images of the entire loading events were documented with a high-speed camera. Three-dimensional X-ray micro-computed tomography was conducted to examine the intact microstructures and obtain the basic material properties of the bone material used for mechanical characterizations. The onset location, where crack initiated, and the subsequent direction, along which the incipient crack propagated, were measured quantitatively using the high-speed X-ray images and the latter was found dependent on the osteon direction significantly. The crack propagation velocities were dependent on crack extension over the entire crack path significantly for all the three directions while the initial velocity for in-plane longitudinal direction was lower than the other two directions. Straight-through crack paths were observed for in-plane longitudinal specimens while the cracks were deflected and twisted in the in-plane transverse direction. For out-of-plane transverse direction, the cracks follow paths with tortuosity fall in between the other two directions, showing a mixed mode of fractures of the former two extreme cases. The toughening mechanisms, visualized by the high-speed X-ray images, and the corresponding fracture toughness, evaluated in terms of fracture initiation toughness and crack growth resistance curve (R-curve), were also found significantly different among the three osteon directions, suggesting an overall transition from brittle to ductile-like fracture behaviors at the dynamic displacement rate (5.4 m/s) as the osteon orientation varies from in-plane longitudinal to out-of-plane transverse, and to in-plane transverse eventually.

42 ENGINEERING↗

Evaluating the bond strength and fracture mechanisms of cold-sprayed zinc coating on AZ91 magnesium substrate via a combined experimental and computational approach

Magnesium (Mg) alloys are ideal candidates for automotive applications due to their high strength to weight ratio, castability, recyclability etc., however, they lack corrosion and oxidation resistance. Solid-state deposition techniques, such as cold spray, have been demonstrated to enhance their corrosion resistance as it relies on the severe plastic deformation of powder particles upon impact with the substrate to form a metallurgical bond with the substrate and within the coating. At cold sprayed interfaces, a heterogeneous microstructure is formed that includes some porosity, oxides and intermetallics which can significantly affect coating performance. Thus, establishing a direct correlation between the interface microstructure and its properties can aid in designing optimal cold spray parameters. In this study, we investigated the microstructure and mechanical properties of a zinc (Zn) coating deposited on a high pressure die cast (HPDC) AZ91 Mg substrate via high resolution scanning transmission electron microscopy, in situ micro-tensile testing, and finite element method (FEM) modeling. Micro-tensile pillars fabricated using the plasma focused ion beam (PFIB) successfully isolates the coating-substrate interface within the gauge length. The average bond strength of Zn-Mg interface was determined to be ∼140 MPa with failure occurring partially at the interface and mostly into the coatings. A detailed microstructural characterization revealed evidence of a strong metallurgical bonding at the Zn-Mg interface and formation of the C14 MgZn 2 laves phase interlayer resulting in a mixed mode of fracture during the micro-tensile experiments. FEM modeling reveals the stress distribution along the interfaces and suggests that a MgZn 2 layer thickness between 200–400 nm is optimum to increase the bond strength and minimize the triaxiality. Such a site-specific interfacial analysis with correlative computational modeling provides crucial insight into the overall performance of cold spray interfaces.

Bond strength↗

Energy Release Rate Approximation for Small Surface Cracks in Three-Dimensional Domains Using the Topological Derivative

The topological derivative describes the variation of a response functional with respect to infinitesimal changes in topology, such as the introduction of an infinitesimal crack or hole. In this three-dimensional fracture mechanics work, we propose an approximation of the energy release rate field associated with a small surface crack of any boundary location, direction, and orientation combination using the topological derivative. Furthermore, this work builds on the work of Silva et al. (“Energy Release Rate Approximation for Small Surface-Breaking Cracks Using the Topological Derivative,” J. Mech. Phys. Solids 59(5), pp. 925–939), in which the authors proposed an approximation of the energy release rate field which was limited to two-dimensional domains. The proposed method is computationally advantageous because it only requires a single analysis. By contrast, current boundary element and finite element-based methods require an analysis for each crack length-location-direction-orientation combination. Furthermore, the proposed method is evaluated on the non-cracked domain, obviating the need for refined meshes in the crack tip region.

42 ENGINEERING↗

Nonlinear analysis and redesign of the mixed-mode bending delamination test

The Mixed Mode Bending (MMB) test uses a lever to simultaneously apply mode I and mode II loading to a split beam specimen. An iterative analysis that accounts for the geometric nonlinearity of the MMB test was developed. The analysis accurately predicted the measured load displacement response and the strain energy release rate, G, of an MMB test specimen made of APC2 (AS4/PEEK). The errors in G when calculated using linear theory were found to be as large as thirty percent in some cases. Because it would be inconvenient to use a nonlinear analysis to analyze MMB data, the MMB apparatus was redesigned to minimize the nonlinearity. The nonlinear analysis was used as a guide in redesigning the MMB apparatus. With the redesigned apparatus, loads were applied through a roller attached to the level and loaded just above the midplane of the test specimen. The redesigned apparatuus has geometric nonlinearity errors of less than three percent, even for materials substantially tougher than APC2. This apparatus was demonstrated by measuring the mixed mode delamination fracture toughness of APC2.

Reeder, J. R.↗