Single Leg Bending Specimens Research Articles

Evaluation of the intergranular crack growth resistance of ultrafine grained tungsten materials

The brittleness of tungsten at room temperature represents a severe challenge particularly for structural applications. Tungsten composites, consisting of foils or wires, overcome this low ductility by utilizing the remarkable mechanical properties of ultrafine grained tungsten materials. A comprehensive understanding of the fracture behaviour of these ultrafine grained tungsten materials is therefore essential for a further development of high performance structural composites. However, the dimensions of specimens used for classical fracture toughness experiments are not applicable to test all important crack growth directions in the case of thin foils and wires, especially, in the direction of the presumably lowest fracture toughness, which is along their characteristically elongated microstructure. Femtosecond laser processing allows to fabricate micro single leg bending specimens, which enable to properly evaluate the fracture toughness in this orientation. The fracture toughness value at crack initiation found for the foil is 2.4 MPam, whereas for the wire a value of 5.3 MPam was determined. In both cases the results are significantly below the values reported for other orientations. This strongly anisotropic fracture behaviour is responsible for the reduced brittle to ductile transition temperature and the delamination induced toughening for crack orientations perpendicular to the elongated ultrafine grained structure. The distinct difference of the fracture toughness at crack initiation and the R-curve between wire and foil specimens could be primarily explained by the morphologies of the fracture surfaces, exhibiting significantly different roughnesses of the evolving crack paths.

Mixed mode fracture characterization of GFRP-concrete bonded interface using four-point single leg bending test

A combined analytical and experimental study using a single leg bending specimen under four-point bend loading is conducted to characterize mixed mode fracture of glass fiber reinforced polymer (GFRP)-concrete bonded interface. Both the conventional composite (rigid joint) and interface deformable (flexible joint) bi-layer beam theories are used to calculate the compliance and energy release rate (ERR) of the proposed four-point single leg bending (4-SLB) specimens which are compared with and verified by the numerical finite element results. The results show that the flexible joint model results in more accurate compliance and ERR compared with the conventional composite bi-layer beam theory for the 4-SLB specimen due to the attribute of crack tip deformation. The calculated ERR by the flexible joint model can be reduced to that of the rigid joint one when the specimen is properly sized. Then, the designed 4-SLB specimens are utilized to measure the fracture toughness of GFRP-concrete bonded interface. To overcome the obstacle of low tensile strength of concrete and prevent the concrete substrate from premature fracture before the crack propagation of GFRP-concrete bonded interface takes place, the steel bars are used to reinforce the concrete substrate beams and a reduced section scheme at the interface is adopted. An aluminum beam is bonded to the thin GFRP plate so as to obtain different fracture mode ratios. The fracture toughness values of GFRP-concrete bonded interface under two different fracture mode ratios are obtained. The proposed 4-SLB specimen and data reduction procedures for the interface fracture toughness evaluation can be used to effectively characterize mixed mode fracture of hybrid material bonded interfaces.

J-integral for delaminated beam and plate models

In this work the J-integral is applied to calculate the energy release rate in simple beam and plate models. Four examples are considered: the mode-I double-cantilever beam, the mode-II end-notched flexure, the mixed-mode I/II single-leg bending specimens and a delaminated plate with simply-supported edges, respectively. In each example the details of calculation are given, in the latter case the distribution of the energy release rate along the crack front is calculated. While for delaminated beams the literature presents the energy release rates in numerous studies, the J-integral calculation is not trivial in theses cases. Moreover for delaminated bent plates the application of the J-integral is not documented. It is shown that considering the classical plate theory there are serious limitations to calculate representative energy release rates.

Linear and nonlinear finite element analyses of unidirectional, symmetric single leg four-point bending tests

Geometrically linear and nonlinear finite element analyses are used to determine the energy release rate and mode ratio in simulated tests of unidirectional, symmetric, single leg bending specimens under four-point bending. It is shown that the finite diameter loading rollers that are typically used in practical test set-ups cause this test to be inherently nonlinear. The differences between the linear and nonlinear results are presented parametrically as a function of material properties, specimen thickness, roller diameter, crack length, and inner and outer span length. The perceived advantages and disadvantages of this test are compared to those of the more commonly used three-point single leg bending test. It is concluded that the four-point test provides an attractive alternative, as it can use the same type of test specimens and will produce toughnesses with essentially the same accuracy. Moreover, it allows non-precracked and precracked toughnesses, as well as R-curve data, to be obtained from each specimen tested.

A shell/3D modeling technique for the analysis of delaminated composite laminates

A shell/3D modeling technique was developed for which a local solid finite element model is used only in the immediate vicinity of the delamination front. The goal was to combine the accuracy of the full three-dimensional solution with the computational efficiency of a shell finite element model. Multi-point constraints provided a kinematically compatible interface between the local 3D model and the global structural model which has been meshed with shell finite elements. Double Cantilever Beam, End Notched Flexure, and Single Leg Bending specimens were analyzed first using full 3D finite element models to obtain reference solutions. Mixed mode strain energy release rate distributions were computed using the virtual crack closure technique. The analyses were repeated using the shell/3D technique to study the feasibility for pure mode I, mode II and mixed mode I/II cases. Specimens with a unidirectional layup and with a multidirectional layup were simulated. For a local 3D model, extending to a minimum of about three specimen thicknesses on either side of the delamination front, the results were in good agreement with mixed mode strain energy release rates obtained from computations where the entire specimen had been modeled with solid elements. For large built-up composite structures the shell/3D modeling technique offers a great potential for reducing the model size, since only a relatively small section in the vicinity of the delamination front needs to be modeled with solid elements.

Nonlinear Analyses of Homogeneous, Symmetrically Delaminated Single Leg Bending Specimens

Energy release rates obtained by geometrically linear and geometrically nonlinear finite element analyses of homogeneous, symmetrically delaminated single leg bending specimens are presented for a variety of materials, specimen geometries and fixture dimensions. It is shown that certain test geometries will exhibit strong nonlinear effects; thus, critical energy release rates obtained from tests of these geometries, using data reduction procedures that are based on linear theory, may contain significant errors. The nonlinear finite element results are used to develop empirical relationships between energy release rate as predicted by the nonlinear analyses and those predicted by linear analyses. These empirical relationships are shown to be valid over a wide range of specimen material properties, material property ratios (e.g., Young's modulus to shear modulus) and geometric properties of both the specimen and fixture, including fixture roller diameters. Thus, the empirical relationships may be used in a quantitative manner to design tests in order that significant nonlinear effects do not occur prior to fracture, and hence linear data reduction procedures remain valid. Alternatively, the empirical relationships may be used to interpret test results where nonlinear behavior occurs. Both uses are illustrated by example for typical laminated composite materials.