On the toughening of brittle materials by grain bridging:promoting intergranular fracture through grain angle, strength, andtoughness

The structural reliability of many brittle materials such asstructural ceramics relies on the occurrence of intergranular, as opposedto transgranular, fracture in order to induce toughening by grainbridging. For a constant grain boundary strength and grain boundarytoughness, the current work examines the role of grain strength, graintoughness, and grain angle in promoting intergranular fracture in orderto maintain such toughening. Previous studies have illustrated that anintergranular path and the consequent grain bridging process can bepartitioned into five distinct regimes, namely: propagate, kink, arrest,stall and bridge. To determine the validity of the assumed intergranularpath, the classical penentration/deflection problem of a crack impingingon an interface is reexamined within a cohesive zone framework forintergranular and transgranular fracture. Results considering both modesof propagation, i.e., a transgranular and intergranular path, reveal thatcrack-tip shielding is a natural outcome of the cohesive zone approach tofracture. Cohesive zone growth in one mode shields the opposing mode fromthe stresses required for cohesive zone initiation. Although stablepropagation occurs when the required driving force is equivalent to thetoughness for either transgranular or intergranular fracture, the mode ofpropagation depends on the normalized grain strength, normalized graintoughness, and grain angle. For each grain angle, the intersection ofsingle path and multiple path solutions demarcates "strong" grains thatincrease the macroscopic toughness and "weak" grains that decrease it.The unstable transition to intergranular fracture reveals that anincreasinggrain toughness requires a growing region of the transgranularcohesive zone be at and near the peak cohesive strength. The inability ofthe body to provide the requisite stress field yields an overdriven andunstable configuration. The current results provide restrictions for theachievement of substantial toughening through intergranularfracture

On the toughening of brittle materials by grain bridging: promoting intergranular fracture through grain angle, strength, and toughness

Abstract The structural reliability of many brittle materials such as structural ceramics relies on the occurrence of intergranular, as opposed to transgranular, fracture in order to induce toughening by grain bridging. For a constant grain boundary strength and grain boundary toughness, the current work examines the role of grain strength, grain toughness, and grain angle in promoting intergranular fracture in order to maintain such toughening. Previous studies have illustrated that an intergranular path and the consequent grain bridging process can be partitioned into five distinct regimes, namely: propagate, kink, arrest, stall and bridge. To determine the validity of the assumed intergranular path, the classical penentration/deflection problem of a crack impinging on an interface is reexamined within a cohesive zone framework for intergranular and transgranular fracture. Results considering both modes of propagation, i.e., a transgranular and intergranular path, reveal that crack-tip shielding is a natural outcome of the cohesive zone approach to fracture. Cohesive zone growth in one mode shields the opposing mode from the stresses required for cohesive zone initiation. Although stable propagation occurs when the required driving force is equivalent to the toughness for either transgranular or intergranular fracture, the mode of propagation depends on the normalized grain strength, normalized grain toughness, and grain angle. For each grain angle, the intersection of single path and multiple path solutions demarcates "strong" grains that increase the macroscopic toughness and "weak" grains that decrease it. The unstable transition to intergranular fracture reveals that an increasing grain toughness requires a growing region of the transgranular cohesive zone be at and near the peak cohesive strength. The Preprint submitted to Journal of the Mechanics and Physics of Solids 30 November 2007 inability of the body to provide the requisite stress field yields an overdriven and unstable configuration. The current results provide restrictions for the achievement of substantial toughening through intergranular fracture

A micromechanical basis for partitioning the evolution of grainbridging in brittle materials

A micromechanical model is developed for grain bridging inmonolithic ceramics. Specifically, bridge formation of a single,non-equiaxed grain spanning adjacent grains is addressed. A cohesive zoneframework enables crack initiation and propagation along grainboundaries. The evolution of the bridge is investigated through avariance in both grain angle and aspect ratio. We propose that thebridging process can be partitioned into five distinct regimes ofresistance: propagate, kink, arrest, stall, and bridge. Although crackpropagation and kinking are well understood, crack arrest and subsequent"stall" have been largely overlooked. Resistance during the stall regimeexposes large volumes of microstructure to stresses well in excess of thegrain boundary strength. Bridging can occur through continued propagationor reinitiation ahead of the stalled crack tip. The driving forcerequired to reinitiate is substantially greater than the driving forcerequired to kink. In addition, the critical driving force to reinitiateis sensitive to grain aspect ratio but relatively insensitive to grainangle. The marked increase in crack resistance occurs prior to bridgeformation and provides an interpretation for the rapidly risingresistance curves which govern the strength of many brittle materials atrealistically small flaw sizes

A mechanism-based approach to modeling ductile fracture.

Ductile fracture in metals has been observed to result from the nucleation, growth, and coalescence of voids. The evolution of this damage is inherently history dependent, affected by how time-varying stresses drive the formation of defect structures in the material. At some critically damaged state, the softening response of the material leads to strain localization across a surface that, under continued loading, becomes the faces of a crack in the material. Modeling localization of strain requires introduction of a length scale to make the energy dissipated in the localized zone well-defined. In this work, a cohesive zone approach is used to describe the post-bifurcation evolution of material within the localized zone. The relations are developed within a thermodynamically consistent framework that incorporates temperature and rate-dependent evolution relationships motivated by dislocation mechanics. As such, we do not prescribe the evolution of tractions with opening displacements across the localized zone a priori. The evolution of tractions is itself an outcome of the solution of particular, initial boundary value problems. The stress and internal state of the material at the point of bifurcation provides the initial conditions for the subsequent evolution of the cohesive zone. The models we develop are motivated by in-situ scanning electron microscopy of three-point bending experiments using 6061-T6 aluminum and 304L stainless steel, The in situ observations of the initiation and evolution of fracture zones reveal the scale over which the failure mechanisms act. In addition, these observations are essential for motivating the micromechanically-based models of the decohesion process that incorporate the effects of loading mode mixity, temperature, and loading rate. The response of these new cohesive zone relations is demonstrated by modeling the three-point bending configuration used for the experiments. In addition, we survey other methods with the potential to provide more detailed information about the near tip deformation fields

A three-dimensional validation of crack curvature in muscovite mica

Experimental and computational efforts focused on characterizing crack tip curvature in muscovite mica. Wedge-driven cracks were propagated under monochromatic light. Micrographs verified the subtle curvature of the crack front near the free surface. A cohesive approach was employed to model mixed-mode fracture in a three-dimensional framework. Finite element calculations captured the crack curvature observed in experiment

Progress report for the ASCI AD resistance weld process modeling project AD2003-15.

This report documents activities related to the ASCI AD Resistance Weld Process Modeling Project AD2003-15. Activities up to and including FY2004 are discussed. This was the third year for this multi year project, the objective of which is to position the SIERRA computational tools for the solution of resistance welding problems. The process of interest is a three-way coupled problem involving current flow, temperature buildup and large plastic deformation. The DSW application is the reclamation stem weld used in the manufacture of high pressure gas bottles. This is the first year the CALAGIO suite of codes (eCALORE, CALORE, and ADAGIO) was used to successfully solve a three-way coupled problem in SIERRA. This report discusses the application of CALAGIO to the tapered bar acceptance problem and a similar but independent tapered bar simulation of a companion C6 experiment. New additions to the EMMI constitutive model and issues related to CALAGIO performance are also discussed

The Design and Evolution of C

micromechanical basis for partitioning th

Journal of the Mechanics and Physics of Solids

A micromechanical basis for partitioning the evolution of grain bridging in brittle material