ch5-EPFM

ch5-EPFM - Elastic-Plastic Fracture Mechanics Introduction...

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Unformatted text preview: Elastic-Plastic Fracture Mechanics Introduction • When does one need to use LEFM and EPFM? • What is the concept of small-scale and large-scale yielding? Contents of this Chapter • The basics of the two criteria used in EPFM: COD (CTOD), and J-Integral (with H-R-R) • Concept of K- and J-dominated regions, plastic zones • Measurement methods of COD and J-integral • Effect of Geometry Background Knowledge • Theory of Plasticity (Yield criteria, Hardening rules) • Concept of K, G and K-dominated regions • Plastic zone size due to Irwin and Dugdal LEFM and EPFM LEFM • In LEFM, the crack tip stress and displacement field can be uniquely characterized by K, the stress intensity factor. It is neither the magnitude of stress or strain, but a unique parameter that describes the effect of loading at the crack tip region and the resistance of the material. K filed is valid for a small region around the crack tip. It depends on both the values of stress and crack size. We noted that when a far field stress acts on an edge crack of width “a” then for mode I, plane strain case σ σ τ π θ θ θ θ θ θ θ x x y y x y I K r R S | T | U V | W | =- + L N M M M M M M M O Q P P P P P P P 2 2 1 2 3 2 1 2 3 2 2 3 2 c o s s i n ( ) s i n ( ) s i n ( ) s i n ( ) s i n ( ) s i n ( ) σ σ ν σ σ zz zz xx yy = = + 0 for plane stress; for plane strain ( ) u u K r k k x y I R S T U V W =- + + - L N M M M M O Q P P P P 2 2 1 2 2 2 1 2 2 2 2 μ π θ θ θ θ 2 cos ( sin ( )) sin ( cos ( )) LEFM concepts are valid if the plastic zone is much smaller than the singularity zones. Irwin estimates Dugdale strip yield model: r K p I ys = 1 2 2 π σ ( ) r K p I ys = 1 8 2 ( ) σ ASTM: a,B, W-a 2.5 , i.e. of specimen dimension. ≥ ( ) K I ys σ 2 r p ≤ 1 50 LEFM cont. Singularity dominated region σ σ τ π x x y y x y I K r R S | T | U V | W | = L N M M M O Q P P P 2 1 1 For =0 θ For = 2 all ij θ θ σ , = EPFM • In EPFM, the crack tip undergoes significant plasticity as seen in the following diagram. sharp tip I d e a l e la s tic b r ittl e b e h a v io r c le a v a g e f r a c tu r e P : A p p lie d l o a d P : Y i e ld lo a d y D isp la c e m e n t, u L o a d r a t i o , P / P y 1 .0 F r a c tu re B lu n t tip L im ite d p la stic ity a t crac k tip , st ill cl e av a g e fra ctu r e D isplacem ent, u L o a d r a t i o , P / P y 1 .0 Frac tu re Blunt tip Void formation & coalescence failure due to fibrous tearing Displacement, u L o a d r a t i o , P / P y 1.0 Fracture l a r g e s c a l e b l u n t i n g L a r g e s c a l e p l a s t i c i t y f i b r o u s r a p t u r e / d u c t i l e f a i l u r e D isp la cem en t, u L o a d r a t i o , P / P y 1 .0 F rac tu re EPFM cont....
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This note was uploaded on 12/11/2011 for the course EML 3004c taught by Professor Staff during the Fall '11 term at FSU.

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ch5-EPFM - Elastic-Plastic Fracture Mechanics Introduction...

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