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On the toughening of brittle materials by grain bridging: Promoting intergranular fracture through grain angle, strength, and toughness |
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| Authors: | JW Foulk III GC Johnson PA Klein RO Ritchie |
| Institution: | aSandia National Laboratory, Livermore, CA 94550, USA bDepartment of Mechanical Engineering, University of California, Berkeley, CA 94720, USA cFranklin Templeton Investments, San Mateo, CA 94403, USA dDepartment of Materials Science and Engineering, University of California, Berkeley, CA 94720, USA eMaterials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA |
| 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 penetration/deflection problem of a crack impinging on an interface is re-examined 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 near the cohesive strength. The 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. |
| Keywords: | Fracture mechanisms Fracture toughness Ceramics Finite elements Crack bridging |
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