Modulus tearing

From the elastic modulus E, the yield stress cSy and the slope of the J resistance curve, it is possible to calculate the tearing modulus Tj [18]. ... 

Jic is the critical value of the near-tip quasi-static fracture parameter J, i.e. the crack initiation toughness. As for ductile materials a stable crack growth can occur at J values several times the value J c, the non-dimensional tearing modulus Tr was proposed for defining the crack growth toughness [26] ... 

The tearing modulus continuously decreases as the fraction of fibres rises (Fig. 17a). That means once the crack is initiated, its propagation is easiest when the fibre concentration is high the J-Aa resistance curves become more and more flat (Fig. 17b). 

Fig. 17 Evolution of the tearing modulus (a) and the J-Aa resistance curves as a function of the concentration of fibres in the DZ matrix.

A stability analysis is presented for circumferential cracks of constant depth in cantilevered pipings. The analysis is based on the tearing modulus concept and the tearing stability criterion. Assuming that the cracked cross-section is subjected to limit moment the crack growth is studied in the case of pipings subjected to impact loading. 

KEY WORDS J-integral, tearing modulus, crack propagation, plastic fracture... 

The J-integral suggested by Rice [11] and crack opening displacement [13] are the parameters most often used to characterize non-linear fracture behaviour of cracked pipes [13,14], In the present study the tearing modulus stability criterion is used. 

Note that sometimes the modulus is called applied tearing modulus. 

Crack stability is assured when the applied tearing modulus is less than its material counterpart at the prescribed J value. 

The material tearing modulus is derived from the materials J-resistance curve, e.g. 

In the present paper we are seeking for simple theoretical predictions of the relationship between crack length and tearing modulus. Since it is reasonable to assume that the material obeys the piece wise linear yield condition developed by R. H. Lance and D. N. Robinson [6]. Although the yield surface strongly depends on the orientation of fibers we confine our attention to the case of circumferential arrangement of fibers in the matrix material, provided ka is the yield stress in the circumferential direction. The yield condition for circumferentially reinforced cylindrical tubes is presented in Fig. 3. Here... 

The exact calculation of the J-integral and the tearing modulus (1) is quite complicated. It was shown by several authors that a good approximation for the J-integral in the case of rotation around a plastic hinge can be presented as [13,14]... 

Here stands for the applied tearing modulus in the case of radial crack growth. 

In the case of a negative value of the tearing modulus the function J = J(c,0) is a decreasing function with respect to c. 

It can be seen from Fig. 6 that the tearing modulus increases when the parameter cracks appear to have the tendency to be stable. Calculations showed that in the range of very small values of the parameter co the tearing modulus has nonnegative values. However, in this case the tube is either very short or has a great diameter. Thus for reasonable values of geometrical parameters the crack propagation is stable, provided the material modulus is positive. It was shown in [13,14], that for the stainless steel is about 200. 

The problem of the stability of a crack in a piping run subject to an internal impact has been studied. Assuming that the crack has spread circumferentially over the tube with constant length in the radial direction the deformation is considered to be axisymmetric. The motion of a generator of the cylinder has been defined making use of the methods of plastic analysis of cylindrical shells. This motion in turn has been employed to calculate the J-integral and tearing modulus for a cylindrical cantilever tube with a crack in the root section. 

Rajab, M.D. and Zahoor, A., (1991), Tearing modulus analysis for pipes containing constant depth internal flaw. J. Pressure Vessel Technology, 113,1,156. 

Molecular weight Good tensile, tear modulus, set Fast mixing... 

There are similar criteria placed upon the amount of crack growth exhibited by the specimen, such that a combination of J and crack growth limits can be described by a box that the test parameters must stay within to be considered valid measurements, shown in Fig. 10.3c. The values of Ju and tearing modulus can then be used in an analysis to predict ductile crack initiation and ductile crack extension behavior of the RPV. 

In a manner similar to the effects of irradiation on the CVN impact toughness, the fracture toughness is reduced by irradiation and exhibits a transition temperature shift as well as a reduction in/i and tearing modulus. Examples of these effects are shown in Figs 10.9a (Nanstad et al, 1992) and 10.9b Hiser et al, 1984) for two western RPV steels, while the effects on WWER steels are similar. As with CVN impact toughness, the effects of irradiation on the fracture toughness of RPV steels are dependent on the radiation sensitivity of the material which is primarily determined by the specific chemical composition. 

Fracture characteristics and deformation behavior of heterophasic ethylene-propylene copolymers as a function of the disprersed phase comp>osition. Polymer, Vol.46, No.22, (October 2005), pp. 9411-9422, ISSN 0032-3861 Ernst H. A. Paris, P.C. Landes J.D. (1981). Estimations on J-integral and Tearing Modulus T from a single specimen test record. Fracture Mechanics Thirteenth Conference ASTM STP 743, Roberts R., (Ed.), p>p. 476-502. 

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