斷裂力學簡介

內容參考達索於2008年出版的ABAQUS斷裂力學講義。

（1）Fracture mechanics is the field of solid mechanics that deals with the behavior of cracked bodies subjected to stresses and strains.

（2）The objective of fracture mechanics is to characterize the local deformation around a crack tip（裂紋尖端） in terms of the asymptotic field（漸進場） around the crack tip scaled by parameters that are a function of the loading and global geometry.

（3）For engineering materials, such as metals, there are two primary modes of fracture: brittle and ductile（脆性斷裂與延性斷裂）.

（4）Linear Elastic Fracture Mechanics (LEFM) considers three distinct fracture modes: Modes I, II, and III.These encompass all possible ways a crack tip can deform.

（5）The objective of LEFM is to predict the critical loads（臨界載荷） that will cause a crack to grow in a brittle material（脆性材料）.

（6）For isotropic, linear elastic materials, LEFM characterizes the local crack-tip stress field in the linear elastic (i.e., brittle) material using a single parameter called the stress intensity factor K（僅用一個參數「應力強度因子」去描述裂紋尖端附近的應力場）.

（7）K （SIF）depends upon the applied stress, the size and placement of the crack, as well as the geometry of the specimen.

（8）When this stress state (i.e., K) becomes critical（臨界值）, a small crack grows ("extends") and the material fails.This critical value is denoted Kc and is known as the fracture toughness（斷裂韌性）.Fracture toughness is strongly dependent on temperature（受溫度影響）.

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（10）The predicted stress state at the crack tip in a linear elastic (brittle) material possesses a square-root singularity.In reality, the crack tip is surrounded by the fracture process zone（即，存在非線性彈性的區域） where plastic deformation and material damage occur（塑性變形與材料損傷）.This is called small-scale yielding（小範圍屈服）.Inside this zone, the LEFM solution is not valid.Outside of this zone (i.e., sufficiently "far" from the fracture process zone), the LEFM is accurate provided the plastic/damage zone is 「small enough.」

（11）Small-scale yielding (SSY) means the region of inelastic deformation at the crack tip is contained well within the zone dominated by the LEFM asymptotic solution（裂紋尖端非彈性變形區域包含在線彈性漸進解所主導的區域的內部）.

（12）For LEFM to be valid, there must be an annular region around the crack tip（裂紋尖端附近的環形區域） in which the asymptotic solution to the linear elasticity problem gives a good approximation（高度近似） to the complete stress field. We can use LEFM results if the region of inelastic deformation near the crack tip is small enough that there is a finite zone outside this region where the LEFM asymptotic solution is accurate.

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