Influences of non-singular stresses on plane-stress near-tip fields for pressure-sensitive materials and applications to transformation toughened ceramics

In this paper, we investigate the effects of the non-singular stress ( T stress) on the mode I near-tip fields for elastic perfectly plastic pressure-sensitive materials under plane-stress and small-scale yielding conditions. The T stress is the normal stress parallel to the crack faces. The yield criterion for pressure-sensitive materials is described by a linear combination of the effective stress and the hydrostatic stress. Plastic dilatancy is introduced by the normality flow rule. The results of our finite element computations based on a two-parameter boundary layer formulation show that the total angular span of the plastic sectors of the near-tip fields increases with increasing T stress for materials with moderately large pressure sensitivity. The T stress also has significant effects on the sizes and shapes of the plastic zones. The height of the plastic zone increases substantially as the T stress increases, especially for materials with large pressure sensitivity. When the plastic strains are considered to be finite as for transformation toughened ceramics, the results of our finite element computations indicate that the phase transformation zones for strong transformation ceramics with large pressure sensitivity can be approximated by those for elastic-plastic materials with no limit on plastic strains. When the T stress and the stress intensity factor K are prescribed in the two-parameter boundary layer formulation to simulate the crack-tip constraint condition for a single-edge notch bend specimen of zirconia ceramics, our finite element computation shows a spear shape of the phase transformation zone which agrees well with the corresponding experimental observation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42782/1/10704_2004_Article_BF00018779.pd

Numerical investigation of 3-D constraint effects on brittle fracture in SE(B) and C(T) specimens

This investigation employs 3-D nonlinear finite element analyses to conduct an extensive parametric evaluation of crack front stress triaxiality for deep notch SE(B) and C(T) specimens and shallow notch SE(B) specimens, with and without side grooves. Crack front conditions are characterized in terms of J-Q trajectories and the constraint scaling model for cleavage fracture toughness proposed previously by Dodds and Anderson. The 3-D computational results imply that a significantly less strict size/deformation limit, relative to the limits indicated by previous plane-strain computations, is needed to maintain small-scale yielding conditions at fracture by a stress- controlled, cleavage mechanism in deep notch SE(B) and C(T) specimens. Additional new results made available from the 3-D analyses also include revised {eta}-plastic factors for use in experimental studies to convert measured work quantities to thickness average and maximum (local) J-values over the crack front

Critical assessment of the application of the J-integral and CTOD concepts to circumferentially cracked copper bars

The aim of this work is to explore experimentally the validity of the concepts of J-integral and crack tip opening displacement for characterizing the stress and strain state at the tip of an axisymmetrical crack in a bar undergoing large plastic strain before crack extension. The tests are made on extruded copper round bars presenting a very high ductility. Three different analytical formulations of the J-integral proposed in the literature for circumferentially cracked bars are compared at initiation of cracking. The limit between shallow crack and deep crack geometries is experimentally demonstrated. It is found that, in neither of these geometries, J and delta CTOD are dominant. However, the ratio J(c)/delta(c) is constant for deep cracks, which suggests an alternative fracture criterion consisting in postulating the dissipation of an average critical energy per unit volume until crack extension

Interfacial fracture toughness of alumina/niobium systems

The interfacial fracture toughness of an alumina/niobium composite has been measured as a function of phase angle. The interface was formed by solid-state bonding bulk Coor's AD-999 fine-grain alumina with a commercial purity niobium at 1600{degrees}C for 0.5 hr under a pressure of 10.5 MPa. The alumina/niobium system has a number of features which makes it ideal for an investigation of interfacial fracture toughness. From HREM data we estimate that the width of the interface is no more than 10 atomic planes. Furthermore the thermal expansion coefficients of the two materials differ by less than 5% so residual stresses due to the bonding process are small. Using symmetric and asymmetric four point bend specimens we have measured the fracture toughness of homogenous alumina and that of the alumina/niobium bimaterial in combinations of in-plane shear and tension. The fracture toughness of the homogenous alumina is relatively insensitive to the loading phase. The measured fracture toughness K{sub c} of the interface, however, depended strongly on phase angle. We were unable to obtain valid alumina/niobium interfacial toughness data at negative phase angles as the fracture initiates in the alumina and not at the interface. In symmetric bending at a phase angle {approx}5{degrees}, we measured a nominal interface toughness of 4.0 MPa{radical}m, comparable to the homogeneous alumina. We found that the toughness increased with loading phase angle to a value of K{sub c} {approx} 9 MPa{radical}m at a phase between 25{degrees} and 40{degrees}. Preliminary calculations and experiments suggest that this effect is due to an asymmetric stress distribution, with respect to the interface, and plastic deformation in the niobium. 12 refs., 9 figs., 1 tab