AAE352_Summer_Lec26 - Practical Fracture Mechanics Josh...

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Practical Fracture Mechanics Josh Dustin 07/21/10 1
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• Motivation for fracture mechanics development • Introduction to LEFM • Experimental methods for LEFM • Application of LEFM to interlaminar fracture in composites Introduction 2
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Motivation Structures Fail – Structural Failure – Material Failure 3
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Theoretical strength of materials based on atomic models Motivation σ σ 10 E c Material Theoretical Ultimate Strength Actual Ultimate Strength Steel: ASTM A514 Steel, grade P 20.5 Gpa 0.828 GPa Aluminum: 6061-T6 6.89 GPa 0.310 GPa ABS Plastic 0.381 GPa 0.031 GPa Structural Adhesive: Loctite H3000 0.117 GPa 0.016 GPa 4
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Motivation Inglis’ solution for stress at the edge of the elliptical hole (x=a.y=0): b a yy 2 1 What happens to the stress as a=b? As b<<a? σ σ a b x y 5
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0.00E+00 5.00E+06 1.00E+07 1.50E+07 2.00E+07 2.50E+07 3.00E+07 3.50E+07 4.00E+07 4.50E+07 -0.001 1.2E-17 0.001 0.002 0.003 0.004 0.005 σ yy (N/mm^2) Distance ahead of crack tip (mm) Normal Stress Ahead of Crack Tip Mesh 1 Mesh 2 Mesh 3 Mesh 4 Motivation Symmetric FE Model (Mesh 1) 6
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• What factors contribute to the discrepancies between theoretical and actual strength of materials? • How can failure predictions be made in the presence of infinite stress? Motivation 7
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• Linear Elastic Fracture Mechanics (LEFM) – Material is assumed to behave perfectly elastic (linearly) – Two approaches: 1) Energy based, 2) Stress based – Both approaches produce equivalent results for elastic materials LEFM 8
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Griffith theory of fracture based on energy required to create new surfaces Griffith Theory of Fracture condition failure the , 0 lim condition critical growth crack for criterion A area, crack new create to required work body in stored energy strain elastic forces external by done work body cracked a for potential Elastic c c c c G G dA dH G A A H dA dH A G H A G H G U W H U W H 9
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Fracture Modes (a) Mode I (b) Mode II (c) Mode III Fracture mechanics classifies crack loading conditions in terms of three separate failure modes: Linear elasticity is assumed, so can apply superposition to decompose complex loading conditions to combinations of the three modes 10
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• Stress field at the crack tip K can be thought of as a measure of the magnitude of the singular stress at the crack tip Geometry and loading conditions will affect K, but the stress is always of the same functional form Stress Intensity Factor 0 ), ( 2 yz xy I yy x O x K 0 ), ( 2 II x O x K 0 ), ( 2 III x O x K Mode I: Mode II: Mode III: x y a K o I Pure Mode I: 11
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• Two approaches are equivalent for linear elastic materials G/K Relation 2 2 2 2 1 8 1 8 1 III II I I K G K G K G stress plane , 1 3 strain plane , 4 3 12
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• Multiple techniques
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This note was uploaded on 01/18/2012 for the course AAE 352 taught by Professor Chen during the Fall '08 term at Purdue University-West Lafayette.

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AAE352_Summer_Lec26 - Practical Fracture Mechanics Josh...

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