# Elastic-Plastic Fracture Mechanics Introduction When does one need to use LEFM a

## Elastic-Plastic Fracture Mechanics Introduction When does one need to use LEFM a

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EPFM In EPFM, the crack tip undergoes significant plasticity as seen in the following diagram. EPFM cont. EPFM applies to elastoc-rate-independent materials, generally in the large-scale plastic de as long as mation. Two parameters are generally used: Crack opening displacement (COD) or crack tip opening displacement (CTOD). J-integral. Both these parameters give geometry independent measure of fracture toughness. Sharp crack Blunting crack y x ds

EPFM cont. Wells discovered that Kic measurements in structural steels required very large thicknesses as long as LEFM condition. — Crack face moved away prior to fracture. — Plastic de as long as mation blunted the sharp crack. Sharp crack Blunting crack Irwin showed that crack tip plasticity makes the crack behave as if it were longer, say from size a to a + rp -plane stress From Table 2.2, Set , Note: since CTOD in addition to strain-energy release rate Equation relates CTOD ( ) to G as long as small-scale yielding. Wells proved that Can valid even as long as large scale yielding, in addition to is later shown to be related to J. can also be analyzed using Dugdales strip yield model. If   is the opening at the end of the strip. Consider an infinite plate with a image crack subject to a Exp in addition to ing in an infinite series, If , in addition to can be given as: In general, Alternative definition of CTOD Sharp crack Blunting crack Blunting crack Displacement at the original crack tip Displacement at 900 line intersection, suggested by Rice CTOD measurement using three-point bend specimen Vp ‘ ‘ ‘ displacement exp in addition to ing

Now, as long as the present problem. Williams Singularity 3 Applying boundary conditions, Case (i) or, Case (ii) Since the problem is linear, any linear combination of the above two will also be acceptable. Thus Though all values are mathematically fine, from the physics point of view, since Williams Singularity 4 Since U should be provided as long as any annular rising behavior in addition to R ,

Williams Singularity 4 Williams Singularity 5 Williams Singularity 6

HRR Singularity 1 HRR Singularity 2

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