Advanced Materials & Processes

NOV-DEC 2013

Covers developments in engineering materials selection, processing, fabrication, testing/characterization, materials engineering trends, and emerging technologies, industrial and consumer applications, as well as business and management trends

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y more pronounced influence on toughness properties in the ductile-to-brittle temperature transition regime. The list of parameters provides an overview of constraint effects on fracture toughness and how they may either increase or decrease a material's measured fracture toughness. Specimen size effect Specimen geometry can have a substantial effect on fracture toughness[6-10] as illustrated in Fig. 4. As specimen thickness increases for a combination of specimen geometry and material where the remaining ligament remains predominantly elastic, fracture toughness reaches a minimum value defined as KIc. When specimen thickness is sufficiently large, plane strain behavior is created, resulting in a potential lower bound result that may or may not be representative of the structure. The specimen thickness at which plane strain behavior is achieved in the specimen is defined as[7, 10, and 11]: t = 2.5 K ( ) 2 y z Fracture toughness Fig. 3 — Stress state at the tip of a crack. t = 2.5 2 KIc Fig. 4 — Effect of specimen thickness on fracture toughness behavior[7 and 11]. Plane stress behavior Ductile fracture Ductile Plane strain behavior Brittle Ductile-to-brittle transition region where t = specimen thickness K = Stress Intensity Factor, fracture toughness of the material y = yield strength of the material The specimen size (thickness) effect is most pronounced in the ductile-to-brittle transition regime as illustrated in Fig. 5. In the transition region, toughness values decrease with increasing thickness until plane strain conditions are achieved in the specimen. A further increase in specimen thickness boosts the volume of highly stressed material and thereby increases cleavage fracture probability. As mentioned previously, plane strain conditions create a higher degree of constraint in the specimen's center. The increased constraint effectively increases the material's local strength, reducing its ability to yield ahead of the crack tip. By restricting this ability, the potential for the material to reach the fracture limit increases, resulting in ( ) K y Specimen thickness Fracture toughness Defining constraint Constraint refers to the stress state at the crack tip. As specimen thickness increases, transverse contraction is inhibited, thereby increasing stress in the thickness direction (z direction in Fig. 3). The resulting triaxial tensile stress state inside the specimen inhibits yielding so that stresses are elevated and the probability of fracture increases in the lower shelf and transition regions. The triaxial character of the stress state is also increased by placing the remaining ligament in bending and by introducing a biaxial stress (parallel to x axis). The term plane strain refers to a stress state with a high triaxial tensile component. Plane stress refers to a stress state where there is no stress in the thickness direction (z direction in Fig. 3). Plane stress conditions occur in thin material that has the ability to contract in the thickness direction, resulting in negligible stress in the z direction. x Brittle fracture Test temperature Fig. 5 — Effect of constraint on fracture toughness behavior[6, 7, 11]. a reduction in the material's fracture toughness. This decrease in fracture toughness is controlled by specimen thickness, even though the inherent metallurgical properties of the material may be the same. This effect is illustrated by the vertical line in Fig. 4. The specimen with low constraint (plane stress behavior) fails by ductile tearing, while a specimen with higher constraint (plane strain behavior) fails by cleavage. Fracture toughness test methods are generally designed to measure lower bound fracture toughness. However, the ADVANCED MATERIALS & PROCESSES • NOVEMBER-DECEMBER 2013 15

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