Introduction to Fracture mechanics
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This document provides an introduction to fracture mechanics. It discusses different types of brittle and ductile fracture, modes of failure, energy release rate and crack resistance, crack growth, stress intensity factor, and the J-integral. It also mentions a case study on liberty ship failures and provides references for further reading. The key topics covered are the assumptions of fracture mechanics, using energy-based approaches like compliance and strain energy to analyze crack growth, and stress intensity factors which characterize how potent a crack is under different loading conditions.
Introduction to Fracture mechanics
- 1. Introduction to Fracture Mechanics Harshal Patil (13ME63R26) Mechanical Systems Design
- 2. Overview Brittle & Ductile Fracture Modes of Failure Energy Release Rate & Crack Resistance Crack Growth Stress Intensity Factor J-integral Case Study References
- 3. Fracture Mechanics • Fracture mechanics is based on the implicit assumption that there exists a crack in a work component • Fracture mechanics deals with the question – is a known crack likely to grow under a certain given loading condition
- 4. Fracture Modes • Classification is based on the ability of a material to experience plastic deformation • Ductile fracture – Accompanied by significant plastic deformation • Brittle fracture – Little or no plastic deformation – Sudden, catastrophic
- 8. How Potent Is The Crack??
- 9. Griffifth’s Realisation 2a • σmax = σo σo 2b • Crack in the body would not grow unless energy was released to overcome the energy needs of forming two new surfaces • Surface energy is of the order of 1 J/m2
- 10. Energy Release Rate • Energy release per unit increase in area during crack growth • LEFM (Linear Elastic Fracture Mechanics) • Conservation of energy, G ΔA = Δ Wext – ΔU G= G= Two approaches are developed Compliance Approach Strain Energy
- 11. Crack Resistance • Energy requirement for a crack to grow per unit area extension • Sum of energy required for Two new surfaces Anelastic deformation • It characterizes the material behavior • It depends on the plastic zone size
- 12. Stable & Unstable Crack Growth For a crack to grow & become critical 1) 2)
- 13. R-curve For Brittle Materials •Negligible size of plastic zone in the vicinity of crack tip •No stable growth if
- 14. Stress Intensity Factor There are two main variables σ - Far Field Stress a - Crack length Irwin defined the new variable, K KI = σ(πa)1/2 KII = τ(πa)1/2 KIII = τ(πa)1/2 Mode-I Mode-II Mode-III G=K2/E (For plane stress)
- 15. SIF for mode I problem Where, KI = σ(πa)1/2
- 16. J Integral • Concept of Energy Release Rate is not applicable to material with large plastic zone at the vicinity of crack tip • EPFM (Elastic Plastic Fracture Mechanics) • Path Independence • G=J (For linear elastic materials only) • J=
- 18. References 1.1 Kumar,P.(2009). Elements of Fracture Mechanics, Tata McGraw Hill, New Delhi. 1.2 Anderson,T.L. (2004).Fracture Mechanics: Fundamentals and Applications, CRC, Press-Book. 1.3 Broek,D.(1982). Elementary Engineering Fracture Mechanics, Martinus Nijhoff Publishers, The Hague.