Pure mode

Figure 7 shows these results schematically for both twist and tilt crack deflections. Thus, for the stress intensity factor required to drive a crack at a tilt or twist angle, the appHed driving force must be increased over and above that required to propagate the crack under pure mode 1 loading conditions. Twist deflection out of plane is a more effective toughening mechanism than a simple tilt deflection out of plane. 

The pure mode II interlaminar fracture testing can be performed using both the end notched flexure (ENF) specimen (Russell and Street, 1984, 1985) and the end loaded split (ELS) specimen (Corleto and Bradley, 1987 Prel et al.. 1989) (Fig 3.32). 

An oscilloscope and a camera were used to record the output voltage of die crystal detector. The oscilloscope was triggered from the ionization switch probe by the detonation and a dielectric rod waveguide (such as described in Ref 18a) was used as a transmission line between the instrumentation and the sample. The dielectric rod waveguide was expandable and acted as a mode selector to launch a pure mode of transmission in the sample. The location of sample, detonator and ionization switch are shown in Fig 30. The standard rectangular waveguide from the instrumentation shown in Fig 29 was converted to circular waveguide by a transition. A polystyrene rod... 

In Example 2.2, Equation 2.11 reduced to equations for three uncoupled modes capable of propagating along the x axis of a cubic crystal. Undm- such conditions, the propagation direction is referred to as a pure-mode direction. In general, pure modes result when waves are propagating along a symmetry plane of a crystal and have polarization perpendicular to or parallel to this plane. Also, propaga-... 

For propagation in an isotropic medium or along a pure-mode direction of a crystal (e.g., a plane of symmetry). Equation 3.38 reduces to a Rayleigh wave, characterized by having no transverse component Ux = 0. Since Uy and Uz are 90° out of phase, the particles move in an elliptical orbit in the sagittal plane die surface motion resembles that of the ocean under the influence of a passing wave. 

As shown in Fig. 15, the mode II fracture toughness, G], was more than twice as high as the mode I fracture toughness, G q. However, the difference was much smaller than that of the other materials such as polymer matrix composite materials. This would be the consequence that the microscopic fracture of the present specimen was not pure mode II owing to the discrepancy between the macroscopic crack face and microscopic crack path even though the mode II loading was applied macroscopically, as suggested by the results shown in Fig. 14. 

Deviations of the delamination from the mid-plane imply mixed-mode conditions, i.e., a deviation from a pure Mode I opening load. The degree of mode mixity will depend on the relative stiffness of the two unequal beams. In the cross-ply laminates, this stiffness difference will be small , as long as the unidirectional plies that essentially provide the axial stiffness are equal in both beams. This is a rational justification for a validity criterion for cross-ply laminates that allows deviations from the mid-plane, as long as the delamination does not show a transition into the unidirectional plies. 

If fracture occurs at a critical value of G, then this implies fracture occurs at a critical value of K for a given mode of loading. For fracture under pure mode I loading, the failure criterion is given by K =T, where T is the fracture toughness of the material. Thus, the failure criterion can be described in a variety of ways, e.g.. 

The above discussion considered cracks from a macroscopic viewpoint but even for a pure mode I loaded crack, cracks are often deflected at a micro-structural level. This crack deflection is a result of variations in the fracture toughness within real materials and the influence of localized stress fields. These observations imply that mixed mode effects can play a role even in a failure that appears to be a result of pure mode I loading, i.e., with the crack propagating normal to the maximum stress. Crack deflection on the microstructural scale are discussed further in the next section. 

Irwin [46] derived the relationship between the strain energy release rate and the stress intensity factor from the stress field at the crack tip. For a pure mode I... 

Of course, an SLB specimen provides more information than the pure Mode I and Mode II fractures, that is, the mixed fracture mode. Therefore, we need to define a new parameter to evaluate the mixed mode healing efficiency. Because the energy release rate is a scalar, we can define the total critical energy release rate, Jc, during the mixed mode fracture process as... 

Ouyang, Z., Ji, G., and Li, G. (2011) On approximately realizing and characterizing pure Mode-I interface fracture between bonded dissimilar materials. ASME Journal of Applied Mechanics, 78, paper 031020. 

The situation is more delicate when the two materials have different moduli. In this case, if the beams are of identical thickness the failure will no longer be purely mode I. In these circumstances the crack will deviate from the interface into the material with the lower deformation resistance, leading to additional energy dissipation. In these circumstances the measured values of the interfacial fracture energy will be larger than Gic- This problem can be overcome by using an asymmetrical test, in which the thicknesses of the two beams are unequal. At a particular ratio of thicknesses the measured fracture energy will be a minimum and this may be taken as the true value of G c. 

The stationary mode, or steady state, is a transfer ensured only by conduction. The temporal mode corresponds to a pnre storage of inductive energy (ultra-thin layer case, i.e., without transport). The other modes mix the two pure modes in various proportions (by complementing paths). 

With the aim to extend the model to mixed-mode I/II conditions, a mixed mode cohesive law has to be defined. This is done according to the scheme shown in Figure 5 from the knowledge of the pure mode I and pure mode II cohesive laws (the index 22, refers to opening or mode I direction, index 12 refers to sliding or mode II direction)... 

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