Stress redistribution

It is noted that Rr is times the Outwater Murphy debonding toughness given 

As the external loading continues and the crack propagates, the broken fibers are pulled out from the matrix (Fig. 6.1(e)), resulting in a continuation of the post- 

Since fiber pull-out length, p , is difficult to measure with any accuracy from the fracture surface of composite specimens containing high V(, Rpo is often expressed in terms of the inherent properties of the composite constituents. There are three cases considered here depending on the fiber length relative to the critical transfer length. 

8) an upper bound estimate of tf is made by the apparent bond strength Tj for the critical transfer length, i.e., 4 fffd/2Tf, based on the early work of Kelly and Tyson (1965). Therefore, Rpo is shown directly proportional to the critieal transfer length. 

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The second physical quantity of interest is, r t = 90 pm, the critical crack tip stress field dimension. Irwin s analysis of the crack tip process zone dimension for an elastic-perfectly plastic material began with the perfectly elastic crack tip stress field solution of Eq. 1 and allowed for stress redistribution to account for the fact that the near crack tip field would be limited to Oj . The net result of this analysis is that the crack tip inelastic zone was nearly twice that predicted by Eq. 3, such that... 

Creep testing of weld joints to determine weld joint strength reduction factors should be full thickness crossweld specimens with test durations of at least 1 000 h. Full thickness tests shall be used unless the designer otherwise considers effects such as stress redistribution across the weld. 

Mai (1985) has also given a review of the fracture mechanisms in cementitious fiber composites. The total fracture toughness, / i, is given by the sum of the work dissipation due to fiber pull-out, fiber and matrix fraetures, fiber-matrix interfacial debonding and stress redistribution, i.e.. 

Dilsizian V, Perrone-Filardi P, Arrighi JA, Bacharach SL, Quyyumi AA, Freedman NM et al. Concordance and discordance between stress-redistribution-reinjection and rest-redistribution thallium imaging for assessing viable myocardium. Comparison with metabolic activity by positron emission tomography. Circulation 1993 88 941-952... 

Dilsizian V, Rocco TP, Freedman NM, Leon MB, Bonow RO. Enhanced detection of ischemic but viable myocardium by the reinjection of thalhum after stress-redistribution imaging. N Engl J Med 1990 323 141-146... 

W. Beere. Stress redistribution during Nabarro-Herring and superplastic creep. Metal Sci., 10(4) 133—139, 1976. 

The initial intent of this review is to address the mechanisms of stress redistribution upon monotonic and cyclic loading, as well as the mechanics needed to characterize the notch sensitivity.5 13 This assessment is conducted primarily for composites with 2-D reinforcements. The basic phenomena that give rise to inelastic strains are matrix cracks and fiber failures subject to interfaces that debond and slide (Fig. 1.1).14-16 These phenomena identify the essential constituent properties, which have the typical values indicated in Table 1.1. 

Fig. 1.2 Three prevalent damage mechanisms occurring around notches in CMCs. Each mechanism allows stress redistribution by a combination of matrix cracking and fiber pull-out.

Background At elevated temperatures the rapid application of a sustained creep load to a fiber-reinforced ceramic typically produces an instantaneous elastic strain, followed by time-dependent creep deformation. Because the elastic constants, creep rates and stress-relaxation behavior of the fibers and matrix typically differ, a time-dependent redistribution in stress between the fibers and matrix will occur during creep. Even in the absence of an applied load, stress redistribution can occur if differences in the thermal expansion coefficients of the fibers and matrix generate residual stresses when a component is heated. For temperatures sufficient to cause the creep deformation of either constituent, this mismatch in creep resistance causes a progres-... 

Application of the 1-D Model Transient Creep and Stress Redistribution... 

It is useful to define a parameter that describes the direction and magnitude of the driving force for stress redistribution. Rather than use the difference in creep rates, it is more convenient to define this parameter as the ratio between the constituent creep rates. For this purpose, a time-dependent... 

The creep rates in Eqn. (11) refer to the in situ creep rates experienced by the fibers and matrix within a composite. Since the creep rates of fibers and matrix are a function of time during the stress redistribution process, the in situ creep... 

The in situ creep mismatch ratio CMR, can provide a quantitative estimate of the driving force for load transfer between constituents. However, it is a rather complicated function of the stress redistribution processes. In order to indicate the basic characteristics of stress redistribution, it is convenient to directly compare the intrinsic (unconstrained) creep rates using the initial elastic stress experienced by the constituents. From Eqn. (12),... 

At elevated temperatures, creep deformation and transient stress redistribution between the fibers and matrix can have a significant influence on... 

The analytical approach developed by Schadler and Noyan, allows calculation of the stress redistribution in cracked triple layer systems. This approach assumes mechanical equilibrium of the cracked coating and the interlayer through perfectly adhering interfaces which transfer the applied stress to the substrate. It is thus possible to deduce expressions for stress distribution normal to the cracked film and shear stress distribution at the interlayer ... 

The energy conservation is thus assured and the stress redistributed in front of the crack tip according to more realistic physical principles. The toughness values can be recalculated with ... 

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