Cracks dimensional analysis

A. Carpinteri et al Cohesive crack model description of ductile to brittle size-scale transition dimensional analysis vs. renormalization group theory. Eng. Fract. Mech. 70(14) 1809-1839 (2003)... 

Fig. 12 Theoretical analysis of initial crack growth directions. In a first step, the three-dimensional elastic contact stress field is calculated within the polymer body under small amplitude reciprocating micro-motions. A two-dimensional analysis of crack initiation is subsequently carried out using the calculated stress values in the meridian plane of the contact (Oxz). Average shear (rm) and tensile (crm) stresses are calculated for different locations in the contact and for different orientations, a, with respect to the normal to the contact plane...

Mathur, K., Needleman, A., and Tvergaard V., Three dimensional analysis of dynamic ductile crack growth in a thin plate, J. Mech. Phys. Solids, 44, 439-464, 1996. 

Kotulla B. et al. Three-dimensional analysis of stresses and crack development in prestressed thick-walled cylinders, 6th Conference on SMIRT, Paris, Paper H3/1, 1981. Cheung K. C. An assessment of long-term structural behaviour of an asymmetric multicavity PCRV, 6th Conference on SMIRT, Paris, August 1981, Paper H3/9, 1981. 

For quantitative analysis, Inglis considered a uniformly stressed two-dimensional solid like a thin plate, containing an elliptic hole representing the crack (see Fig. 3.4). Let the lengths of the semi-major and -minor axes of the ellipse to be 21 and 2b repectively, and a denote the external (say tensile) stress applied on the sample along the y-direction. We assume the (linear) Hooke law to hold everywhere in the plate and that the boundary surface of the elliptic hole, represented by the equation... 

In a three-dimensional solid containing a single elliptic disk-shaped planar crack perpendicular to the applied tensile stress direction, a straightforward extension of the above analysis suggests that the maximum stress concentration would occur at the two tips (at the two ends of the major axis) of the ellipse. The Griffith stress for the brittle fracture of the solid would therefore be determined by the same formula (3.3), with the crack length 21 replaced by the length of the major axis of the elliptic planar crack. 

In this paper we have calculated the three dimensional stress fields at the tip of the crack associated with the standing waves across the plate, assuming the waves modulate the stress intensity factor of the crack. Thus the present analysis takes account of these important experimental observations for the microcrack branching instability described above. We are unable, however, to clarify the direct cause of this instability but we have pointed out that the transient interference pattern of the standing waves could enhance the stress fields at the tip of the crack, as shown in Fig. 5, and possibly change the dynamics of the propagating crack. 

Most of the crack problems that have been solved are based on two-dimensional, linear elasticity (i.e., the infinitesimal or small strain theory for elasticity). Some three-dimensional problems have also been solved however, they are limited principally to axisymmetric cases. Complex variable techniques have served well in the solution of these problems. To gain a better appreciation of the problems of fracture and crack growth, it is important to understand the basic assumptions and ramifications that underlie the stress analysis of cracks. 

Sato, A., Hirakawa, Y. and Sugawara, K. 2(X)1. Mixed mode crack propagation of homogenized cracks by the two-dimensional DDM analysis. Construction and Building Materials, 15(5-6), pp.247-261. 

Very often a great deal of dimensional information can be found by means of microscopy. which is such an important subject in its own right as to be in no way considered here as a branch of physical testing. For example, one would expect to employ a microscope to determine the thickness of a wax film on the surface of a rubber or to study the geometry of fibers or thin film, and much failure analysis involves detailed optical e.xam-ination. There are inevitably a great number of special circumstances connected with polymers where an unusual type of dimensional measurement is required, such as the footprint area of tires or the crack length in fracture tests, A number of methods of interest will be mentioned in later chapters in conjunction with particular physical tests. 

Ultrasonic analysis of polymeric materials has been carried out from vanous viewpoints. One of present authors (KM) has performed prease measurements of ultrasonic velocity under tensile stress condition and utilized an acoustic emission (AE) phenomenon to investigate the formation of microscopic cracks and the fracturing process of polymers [1] Instrumental advancements have also enabled us to conduct rapid and even two-dimensional ultrasonic analysis of polymeric materials including composite materials [2,3],... 

Our approach of modeling the diffusion process is divided into the following steps. First, based on the volume fraction of the TP within the thermoset matrix, we can calculate the amount of TP available to flow into the crack using stereology and statistics [31]. The minimum amount of TP needed is determined in such a way that the volume of the available TP, i.e., the TP that can migrate into the crack, is equal to the volume of the crack. Otherwise, only a portion of the crack can be filled and only a portion of the crack surface can be wetted. Second, based on the surface area that is wetted, we will conduct a one-dimensional difrusion analysis. 

More than 10 years ago, the two-dimensional (2D) laser imaging technology was introduced to pavement surface analysis, particularly for cracking surveying (Wang 2000 Wang... 

Nucleation of cracks can be kinematically analyzed by the moment analysis. Applying the SiGMA (Simplified Green s functions for Moment tensor Analysis) code, crack kinematics on locations, t5 es and orientations are determined three-dimensionally. Basic treatment and theoretical background are discussed, including the two-dimensional case. 

In contrast to the effort devoted to surface cracks in cylindrical specimens, internal cracks have attracted less attention from researchers. The available solutions for the stress intensity factor are of circular cracks centred on the fibre axis (Collins, 1962 Sneddon and Tait, 1963). Only recently, a three-dimensional numerical analysis was made to compute K along the crack front of an eccentric circular internal crack under uniaxial tension (Guinea et al., 2002a). 

Thus, toughness, measured and expressed by Kic, is dependent on the elastic modulus, E, of the material, its hardness, H, (microindentation is often preferable for the proper evaluation of the indentation crack), crack length, c, and the applied load. Anstis et al. [11] employed a two-dimensional fracture mechanics analysis. The crack length, c, is measmed from the center of the impression to the crack tip in meters E is in GPa and H is the Vickers hardness in GPa. The height of the opposite triangular faces is h. It is clear that under small indentation loads, only small cracks form, as indicated schematically in Fig. 2.12. Actual Vickers indentation cracks are shown in Fig. 2.13. Equation (2.8) is often also expressed as ... 

Z. H. JIa, D. J. Shippy and F. J. Rizzo, "Three-dimensional crack analysis using singular boundary elements," Int. J. Numer. Methods 28(10), 2257-2273 (1989). 

M. L. Luchi and S. Rizzuti, "Boundary elements for three-dimensional crack analysis," Int. J. Numer. Methods Engrg. 24(12), 2253-2271 (1987). 

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