Crack Bridging Stress Research Articles

Crack growth in alumina at high temperature

The trailing fracture process zone associated with stable crack growth at room and elevated temperature in high density polycrystalline alumina was analyzed by a hybrid experimental-numerical procedure. The experimental and numerical procedures involved moiré interferometry and finite element analyses, respectfully. The crack bridging stress and the dissipated energy in the fracture process zone were determined at room temperature, 600°C, 800°C and 1000°C. Both quantities decreased at elevated temperature due to grain boundary sliding.

Hybrid method in elastic and elastoplastic fracture mechanics

The utility of the hybrid experimental–numerical method in elastic and elastoplastic fracture mechanics is demonstrated through a fracture process zone analysis and a J-integral computation, respectively. For the former, the crack bridging stresses in the fracture process zones of concrete and alumina fracture specimens were determined through an inverse analysis and the dissipated energies in these zones were quantified. For the latter, J-integral was shown to be highly path dependent with stable crack growth.

Preparation and mechanical properties of Al2O3 reinforced by submicrometer Co particles

Al2O3/Co composites were fabricated by vacuum hot-pressing a mixture of α-Al2O3 powder and a fine cobalt powder. Submicron-sized cobalt particles were uniformly dispersed into the Al2O3 matrix, and the dispersed type was a more inter-/intragranular one with increases of cobalt content up to 40 wt% Co addition. The growth of cobalt particles occurred with increasing cobalt content. At 50 wt% Co addition, however, the growth as well as coalescence of cobalt particles occurred. The phases formed in the Al2O3/Co composites were f-Co(fcc), h-Co(hcp), α-Al2O3, and a small amount of graphite. Significant improvements in bending strength (from 341 to 771 MPa) and fracture toughness (from 3.7 to 6.7 MPaċm1/2) of the Al2O3/40 wt% Co(23 vol% Co) composite compared to monolithic Al2O3 were achieved by dispersing submicron-sized Co particles into the Al2O3 matrix. The improvement in bending strength was attributed to the compressive thermal residual stress in the matrix Al2O3 induced by the mismatch of the coefficients of thermal expansion (CTE) between the matrix Al2O3 grains and cobalt particles during cooling from hot-pressing temperature. The fracture toughness of the composite was enhanced by crack bridging, crack deflection, and compressive thermal residual stress.

Determination of Crack Bridging Stresses from Crack Opening Displacement Profiles

This paper discusses the development of an optimization procedure to deduce the bridging stress from the crack opening displacements (COD) measured during fatigue crack growth. Finite element analysis was conducted using the center-cracked geometry to verify the optimization procedure. The proposed procedure successfully predicted the bridging stress distributions with zero stresses at the crack tip and the bridging stress distributions with non-zero stresses at the crack tip. The results also showed that COD measurements spaced at ≈ 0.8-1.0 mm are sufficient for reliable prediction of bridging stresses. Accurate prediction of bridging stresses near the crack tip required COD data within ≈ 0.1 mm from the crack tip. The application of the proposed procedure to a metal matrix composite (SCS-6/TIMETAL®21S) is also discussed.

Subcritical fatigue crack growth in alumina—II. Crack bridging and cyclic fatigue mechanisms

A crack re-notching procedure based on the “hinged straight crack” approximation is used to determine the distribution and magnitude of the bridging traction, σ( X), existing over the faces of the fatigue cracks grown in the experiments of Part I. From this distribution, the σ( u) relation between the bridging tractions and the crack opening is obtained and a simple method is tentatively proposed to measure the magnitude of the crack bridging stress intensity factor, K b. The characteristics of the σ( X) and σ ( u) relations are discussed in the light of the microscopical observations of crack profiles and in terms of the distribution of the frictional and elastic ligaments existing along the faces of the cracks. Crack growth rates and behaviour under different values of stress ratio R are compared and mechanisms of fatigue crack growth vs static crack growth are proposed.

A note on short-crack generation techniques: James, M.N. Mater. Sci. Eng. A Oct. 1991 A417, (1), L13–L16

For monolithic, grain-bridging ceramics, the crack-size dependence of the fatigue threshold during bridging zone development presents a difficulty in its application in design. This paper demonstrates how a fatigue threshold R-curve may express this crack-size dependence, analogous to the traditional fracture toughness R-curve, and may be used to predict the endurance limit and retained strength under cyclic loading conditions. Furthermore, the fatigue threshold R-curve may be deduced from the behavior of millimeter-scale, through-thickness, fatigue cracks via an accurately measured crack bridging stress profile. Both an alumina ceramic with large steady-state bridging zones (∼2 mm), where the predicted and experimentally measured fatigue threshold R-curves agree well over a range of crack sizes from 0.06 to 7 mm, and a (Y2O3-MgO)-doped Si3N4 ceramic, where bridging zones are much shorter (∼100 μm), are investigated. The approach provides a useful alternative to performing difficult short-crack fatigue experiments, particularly for materials with small bridging zones.

Effect of fiber inclination on crack bridging stress in brittle fiber reinforced brittle matrix composites

The mechanical behavior of brittle matrix composites is strongly affected by the bridging of cracks by fibers. In random fiber composites, fibers can lie at an angle to the crack plane. Under such conditions, the bridging stress for a certain crack opening is governed by various micromechanisms including fiber debonding, fiber bending and rupture as well as matrix spalling. While fiber debonding has been widely investigated, the coupled fiber bending/matrix spalling mechanism has received little attention. In this paper, the fiber bending/matrix spalling mechanism is analyzed by treating the fiber as a beam bent on an elastic foundation with variable stiffness and the possibility of spalling. The foundation stiffness and spalling criterion are derived from a finite element analysis. The bridging stress due to bending alone as well as the total bridging stress are then obtained for the case with brittle fibers. Through this analysis, the effect of various microstructural parameters (such as fiber and matrix moduli, matrix spalling strain and fiber/matrix interfacial friction) on the behavior of random fiber composites can be studied. Prediction of maximum bridging stress for inclined fibers based on the present model is shown to be in good agreement with experimental results.

The mechanics of toughness development in ductile phase reinforced brittle matrix composites

This study is a numerical exercise to theoretically analyze toughening in brittle materials consisting of ductile reinforcements, on the basis of crack bridging by ductile particles. The effects of the particle constitute behavior, the shape of the stress-displacement law, the matrix fracture toughness and the overall elastic modulus of the composite on toughness have been illustrated by simple fracture mechanics calculations of self-consistent crack opening displacement profiles and crack bridging stress distributions. An approach to calculate the crack surface displacements, crack bridging stresses and stress intensity factors in any specimen geometry, using weight functions, is presented. Different types of idealized particle stress-displacement responses were used in the calculations. The opening characteristics of a bridge crack and the evolution of toughness for these types have been examined. The conditions for maximum bridging and toughness as well as the conditions at which a fully bridged crack transforms to a partially bridged one have been identified. The role of individual parameters used in constructing the stress-displacement law on composite toughness has been assessed. The toughness has been found to manifest from a complex interaction of the matrix fracture toughness, the composite modulus and the flow behavior of the ductile particle.